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Articles 4411 - 4440 of 5273
Full-Text Articles in Computer Sciences
Zero-Sum Two-Player Game Theoretic Formulation Of Affine Nonlinear Discrete-Time Systems Using Neural Networks, S. Mehraeen, T. Dierks, S. Jagannathan, M. L. Crow
Zero-Sum Two-Player Game Theoretic Formulation Of Affine Nonlinear Discrete-Time Systems Using Neural Networks, S. Mehraeen, T. Dierks, S. Jagannathan, M. L. Crow
Electrical and Computer Engineering Faculty Research & Creative Works
In this paper, the nearly optimal solution for discrete-time (DT) affine nonlinear control systems in the presence of partially unknown internal system dynamics and disturbances is considered. the approach is based on successive approximate solution of the Hamilton-Jacobi-Isaacs (HJI) equation, which appears in optimal control. Successive approximation approach for updating control input and disturbance for DT nonlinear affine systems are proposed. Moreover, sufficient conditions for the convergence of the approximate HJI solution to the saddle-point are derived, and an iterative approach to approximate the HJI equation using a neural network (NN) is presented. Then, the requirement of full knowledge of …
Mahalanobis Taguchi System (Mts) As A Prognostics Tool For Rolling Element Bearing Failures, Ahmet Soylemezoglu, Sarangapani Jagannathan, Can Saygin
Mahalanobis Taguchi System (Mts) As A Prognostics Tool For Rolling Element Bearing Failures, Ahmet Soylemezoglu, Sarangapani Jagannathan, Can Saygin
Electrical and Computer Engineering Faculty Research & Creative Works
In this paper, a novel Mahalanobis-Taguchi system (MTS)-Based fault detection, isolation, and prognostics scheme is presented. the proposed data-driven scheme utilizes the Mahalanobis distance (MD)-Based fault clustering and the progression of MD values over time. MD thresholds derived from the clustering analysis are used for fault detection and isolation. When a fault is detected, the prognostics scheme, which monitors the progression of the MD values, is initiated. Then, using a linear approximation, time to failure is estimated. the performance of the scheme has been validated via experiments performed on rolling element bearings inside the spindle headstock of a microcomputer numerical …
State Variable Distributed-Parameter Representation Of Transmission Line For Transient Simulations, Mehmet Sali̇h Mami̇ş, Asim Kaygusuz, Muhammet Köksal
State Variable Distributed-Parameter Representation Of Transmission Line For Transient Simulations, Mehmet Sali̇h Mami̇ş, Asim Kaygusuz, Muhammet Köksal
Turkish Journal of Electrical Engineering and Computer Sciences
In this paper, a distributed-parameter state variable approach is used to calculate transients on transmission lines based on the concept of travelling waves. The method of characteristics for lossless line is used and the state equations are derived for the system. These equations are converted to a set of difference equations using the trapezoidal rule of integration and solved in time domain using LU decomposition. Single- and multi-phase transmission lines with various linear and non-linear terminations are considered in the illustrative examples. State-space modeling of transposed lines using modal decomposition is introduced and the effects caused by lumped parameter approximation …
An Approach Based On Particle Swarm Computation To Study The Nanoscale Dg Mosfet-Based Circuits, Fayacl Djeffal, Toufik Bendib, Redha Benzid, Abdelhamid Benhaya
An Approach Based On Particle Swarm Computation To Study The Nanoscale Dg Mosfet-Based Circuits, Fayacl Djeffal, Toufik Bendib, Redha Benzid, Abdelhamid Benhaya
Turkish Journal of Electrical Engineering and Computer Sciences
The analytical modeling of nanoscale Double-Gate MOSFETs (DG) requires generally several necessary simplifying assumptions to lead to compact expressions of current-voltage characteristics for nanoscale CMOS circuits design. Further, progress in the development, design and optimization of nanoscale devices necessarily require new theory and modeling tools in order to improve the accuracy and the computational time of circuits' simulators. In this paper, we propose a new particle swarm strategy to study the nanoscale CMOS circuits. The latter is based on the 2-D numerical Non-Equilibrium Green's Function (NEGF) simulation and a new extended long channel DG MOSFET compact model. Good agreement between …
Asynchronous Particle Swarm Optimization-Based Search With A Multi-Robot System: Simulation And Implementation On A Real Robotic System, Sali̇h Burak Akat, Veysel Gazi̇, Lino Marques
Asynchronous Particle Swarm Optimization-Based Search With A Multi-Robot System: Simulation And Implementation On A Real Robotic System, Sali̇h Burak Akat, Veysel Gazi̇, Lino Marques
Turkish Journal of Electrical Engineering and Computer Sciences
In this article we consider a version of the Particle Swarm Optimization (PSO) algorithm which is appropriate for search tasks of multi-agent systems consisting of small robots with limited sensing capability. The proposed method adopts asynchronous mechanism for information exchange and position (way point) updates of the agents. Moreover, at each (information exchange) step the agents communicate with only a possibly different subset of the other agents leading to a dynamic neighborhood topology. We implement the algorithm using the Player/Stage realistic robot simulator as well as on real KheperaIII robots using experimentally collected realistic data of ethanol gas concentration. Simulation …
Optimal Control Of Affine Nonlinear Continuous-Time Systems Using An Online Hamilton-Jacobi-Isaacs Formulation, T. Dierks, Sarangapani Jagannathan
Optimal Control Of Affine Nonlinear Continuous-Time Systems Using An Online Hamilton-Jacobi-Isaacs Formulation, T. Dierks, Sarangapani Jagannathan
Electrical and Computer Engineering Faculty Research & Creative Works
Solving the Hamilton-Jacobi-Isaacs (HJI) equation, commonly used in ℋ∞ optimal control, is often referred to as a two-player differential game where one player tries to minimize the cost function while the other tries to maximize it. in this paper, the HJI equation is formulated online and forward-in-time using a novel single online approximator (SOLA)-Based scheme to achieve optimal regulation and tracking control of affine nonlinear continuous-time systems. the SOLA-Based adaptive approach is designed to learn the infinite horizon HJI equation, the corresponding optimal control input, and the worst-case disturbance. a novel parameter tuning algorithm is derived which not only achieves …
Decentralized Nearly Optimal Control Of A Class Of Interconnected Nonlinear Discrete-Time Systems By Using Online Hamilton-Bellman-Jacobi Formulation, S. Mehraeen, Sarangapani Jagannathan
Decentralized Nearly Optimal Control Of A Class Of Interconnected Nonlinear Discrete-Time Systems By Using Online Hamilton-Bellman-Jacobi Formulation, S. Mehraeen, Sarangapani Jagannathan
Electrical and Computer Engineering Faculty Research & Creative Works
In this paper, the direct neural dynamic programming technique is utilized to solve the Hamilton Jacobi-Bellman (HJB) equation online and forward-in-time for the decentralized nearly optimal control of nonlinear interconnected discrete-time systems in affine form with unknown internal subsystem and interconnection dynamics. Only the state vector of the local subsystem is considered measurable. the decentralized optimal controller design for each subsystem consists of an action neural network (NN) that is aimed to provide a nearly optimal control signal, and a critic NN which approximates the cost function. the NN weights are tuned online for both the NNs. It is shown …
Output Feedback Control Of A Quadrotor Uav Using Neural Networks, Travis Dierks, Sarangapani Jagannathan
Output Feedback Control Of A Quadrotor Uav Using Neural Networks, Travis Dierks, Sarangapani Jagannathan
Electrical and Computer Engineering Faculty Research & Creative Works
In this paper, a new nonlinear controller for a quadrotor unmanned aerial vehicle (UAV) is proposed using neural networks (NNs) and output feedback. the assumption on the availability of UAV dynamics is not always practical, especially in an outdoor environment. Therefore, in this work, an NN is introduced to learn the complete dynamics of the UAV online, including uncertain nonlinear terms like aerodynamic friction and blade flapping. Although a quadrotor UAV is underactuated, a novel NN virtual control input scheme is proposed which allows all six degrees of freedom (DOF) of the UAV to be controlled using only four control …
Optimal Control Of Affine Nonlinear Continuous-Time Systems, T. Dierks, Sarangapani Jagannathan
Optimal Control Of Affine Nonlinear Continuous-Time Systems, T. Dierks, Sarangapani Jagannathan
Electrical and Computer Engineering Faculty Research & Creative Works
In this paper, the optimal regulation and tracking control of affine nonlinear continuous-time systems with known dynamics is undertaken using a novel single online approximator (SOL)-Based scheme. the SOLA-Based adaptive approach is designed to learn the infinite horizon continuous time Hamilton-Jacobi-Bellman (HJB) equation and its corresponding optimal control input. a novel parameter tuning algorithm is derived which not only ensures the optimal cost (HJB) function and control input are achieved, but also ensures the system states remain bounded during the online learning process. Lyapunov techniques show that all signals are uniformly ultimately bounded (UUB) and the approximated control signal approaches …
Novel Dynamic Representation And Control Of Power Systems With Facts Devices, Shahab Mehraeen, Jagannathan Sarangapani, Mariesa Crow
Novel Dynamic Representation And Control Of Power Systems With Facts Devices, Shahab Mehraeen, Jagannathan Sarangapani, Mariesa Crow
Electrical and Computer Engineering Faculty Research & Creative Works
FACTS devices have been shown to be useful in damping power system oscillations. However, in large power systems, the FACTS control design is complex due to the combination of differential and algebraic equations required to model the power system. In this paper, a new method to generate a nonlinear dynamic representation of the power network is introduced to enable more sophisticated control design. Once the new representation is obtained, a back stepping methodology for the UPFC is utilized to mitigate the generator oscillations. Finally, the neural network approximation property is utilized to relax the need for knowledge of the power …
Trust Account Fraud And Effective Information Security Management, Sameera Mubarak
Trust Account Fraud And Effective Information Security Management, Sameera Mubarak
Journal of Digital Forensics, Security and Law
The integrity of lawyers’ trust accounts has come under scrutiny in the last few years. There are strong possibilities of information technology security breaches happening within the firms, either accidental or deliberate. The damage caused by these security breaches could be extreme. For example, a trust account fund in an Australian law firm was misused in a security breach in which Telstra charged A$50,000 for phone usage, mainly for ISD calls to Hong Kong. Our study involved interviewing principals of ten law companies to find out solicitors’ attitudes to computer security and the possibility of breaches of their trust accounts. …
Forensic Analysis Of The Windows 7 Registry, Khawla A. Alghafli, Andrew Jones, Thomas A. Martin
Forensic Analysis Of The Windows 7 Registry, Khawla A. Alghafli, Andrew Jones, Thomas A. Martin
Journal of Digital Forensics, Security and Law
The recovery of digital evidence of crimes from storage media is an increasingly time consuming process as the capacity of the storage media is in a state of constant growth. It is also a difficult and complex task for the forensic investigator to analyse all of the locations in the storage media. These two factors, when combined, may result in a delay in bringing a case to court. The concept of this paper is to start the initial forensic analysis of the storage media in locations that are most likely to contain digital evidence, the Windows Registry. Consequently, the forensic …
Reeling In Big Phish With A Deep Md5 Net, Brad Wardman, Gary Warner, Heather Mccalley, Sarah Turner, Anthony Skjellum
Reeling In Big Phish With A Deep Md5 Net, Brad Wardman, Gary Warner, Heather Mccalley, Sarah Turner, Anthony Skjellum
Journal of Digital Forensics, Security and Law
Phishing continues to grow as phishers discover new exploits and attack vectors for hosting malicious content; the traditional response using takedowns and blacklists does not appear to impede phishers significantly. A handful of law enforcement projects — for example the FBI's Digital PhishNet and the Internet Crime and Complaint Center (ic3.gov) — have demonstrated that they can collect phishing data in substantial volumes, but these collections have not yet resulted in a significant decline in criminal phishing activity. In this paper, a new system is demonstrated for prioritizing investigative resources to help reduce the time and effort expended examining this …
The 2009 Analysis Of Information Remaining On Disks Offered For Sale On The Second Hand Market, Andy Jones, Craig Valli, Glenn S. Dardick, Iain Sutherland, G. Dabibi, Gareth Davies
The 2009 Analysis Of Information Remaining On Disks Offered For Sale On The Second Hand Market, Andy Jones, Craig Valli, Glenn S. Dardick, Iain Sutherland, G. Dabibi, Gareth Davies
Journal of Digital Forensics, Security and Law
The ever increasing use and reliance upon computers in both the public and private sector has led to enormous numbers of computers being disposed of at the end of their useful life within an organisation. As the cost of computers has dropped, their use in the home has also continued to increase. In most organisations, computers have a relatively short life and are replaced on a regular basis with the result that, if not properly cleansed of data, they are released into the public domain containing data that can be relatively up to date. This problem is exacerbated by the …
Computer Forensics For Graduate Accountants: A Motivational Curriculum Design Approach, Grover S. Kearns
Computer Forensics For Graduate Accountants: A Motivational Curriculum Design Approach, Grover S. Kearns
Journal of Digital Forensics, Security and Law
Computer forensics involves the investigation of digital sources to acquire evidence that can be used in a court of law. It can also be used to identify and respond to threats to hosts and systems. Accountants use computer forensics to investigate computer crime or misuse, theft of trade secrets, theft of or destruction of intellectual property, and fraud. Education of accountants to use forensic tools is a goal of the AICPA (American Institute of Certified Public Accountants). Accounting students, however, may not view information technology as vital to their career paths and need motivation to acquire forensic knowledge and skills. …
Table Of Contents
Journal of Digital Forensics, Security and Law
No abstract provided.
An Investigation Of Multiple Integration Techniques For Information Systems: A Model For Integrating Data Warehousing, Erp, And Soa In Practice, Jessie Burns
CCAC Theses and Dissertations
This study addressed issues associated with implementing multiple data integrators. The process included implementing the same data integrator multiple times or implementing multiple different data integrators. It was shown that single data integrators implementations were failing at high rates. Environments were complicated because there were more acquisitions and mergers now than in the past, companies were required to be competitive while implementations were taking place, and possibly had short implementation time frames.
The main goal of this study was to develop an agile, sturdy, and rigorous model that addressed the needs of companies that found themselves in situations where they …
Differential Power Analysis Resistant Hardware Implementation Of The Rsa Cryptosystem, Kekli̇k Alpteki̇n Bayam, Berna Örs
Differential Power Analysis Resistant Hardware Implementation Of The Rsa Cryptosystem, Kekli̇k Alpteki̇n Bayam, Berna Örs
Turkish Journal of Electrical Engineering and Computer Sciences
In this paper, RSA cryptosystem was implemented on hardware, then modified to be resistant against Differential Power Analysis attacks by using the Randomized Table Window method. This is the first FPGA realization of an algorithmic countermeasure which makes RSA resistant to power analysis attacks. Modular exponentiation is realized with Montgomery Modular Multiplication. The Montgomery modular multiplier has been realized with Carry-Save Adders. Carry-Save representation has been used throughout the RSA encryption algorithm. The primarily implemented RSA architecture prevents the extraction of the secret key using Simple Power Analysis attacks. When comparing the protected implementation with the unprotected, it can be …
Experimental Studies Of A Scaled-Down Tsr-Based Svc And Tcr-Based Svc Prototype For Voltage Regulation And Compensation, Ayetül Gelen, Tankut Yalçinöz
Experimental Studies Of A Scaled-Down Tsr-Based Svc And Tcr-Based Svc Prototype For Voltage Regulation And Compensation, Ayetül Gelen, Tankut Yalçinöz
Turkish Journal of Electrical Engineering and Computer Sciences
In this paper, prototypes of two shunt flexible AC transmission system (FACTS) devices, a thyristor switched reactor (TSR)-based static VAr compensator (SVC) and a thyristor controlled reactor (TCR)-based static VAr compensator- have been developed. The design and testing of both a TSR-based SVC and a TCR-based SVC are accomplished in the Power Systems Research Laboratory of Nigde University. The TSR-based SVC and TCR-based SVC devices are studied in three-bus and single machine infinite bus systems for three-phase static load conditions. The effects of TSR-based SVC and TCR-based SVC devices on load voltages are also analyzed. Experimental results show that significant …
An Rfid Based Indoor Tracking Method For Navigating Visually Impaired People, Ruşen Öktem, Eli̇f Aydin
An Rfid Based Indoor Tracking Method For Navigating Visually Impaired People, Ruşen Öktem, Eli̇f Aydin
Turkish Journal of Electrical Engineering and Computer Sciences
This paper tackles the RFID based tracking problem in an obscured indoor environment. The proposed solution is an integral part of a navigation aid for guiding visually impaired people in a store. It uses RF signal strengths and is based on the Bayes Decision Theory. An observation vector is formed by received radio signal strength indication values, transmitted from three transmitters at distinct frequencies in the UHF band. The indoor area is divided into square grids, where each grid is considered as a class. The problem of tracking is expressed as classifying the observed radio signal strengths to the most …
Oceanography Radar System Wera: Features, Accuracy, Reliability And Limitations, Thomas Helzel, Matthias Kniephoff, Leif Petersen
Oceanography Radar System Wera: Features, Accuracy, Reliability And Limitations, Thomas Helzel, Matthias Kniephoff, Leif Petersen
Turkish Journal of Electrical Engineering and Computer Sciences
The WERA system (WavE RAdar) is a shore based remote sensing system to monitor ocean surface currents, waves and wind direction. This long range, high resolution monitoring system based on short radio wave radar technology. The vertical polarised electromagnetic wave is coupled to the conductive ocean surface and follows the curvature of the earth. This over the horizon oceanography radar can pick up back-scattered signals from the rough ocean surface (Bragg effect) from ranges of up to 200 km. The physical background, technical concept and environmental boundary conditions are explained. Results for various installations from all over the world demonstrates …
Modeling And Simulation Strategies In High Frequency Surface Wave Radars, Levent Sevgi̇
Modeling And Simulation Strategies In High Frequency Surface Wave Radars, Levent Sevgi̇
Turkish Journal of Electrical Engineering and Computer Sciences
Surface Wave High Frequency Radars (SWHFR) are taken into account in the content of modeling and simulation challenges. Examples related to multi-mixed path surface wave propagation, radar cross section (RCS) prediction, and total radar echo showing target, clutter, noise, and interference are presented.
Implementation Of Method For Operating Multiple High Frequency Surface Wave Radars On A Common Carrier Frequency, Ryan Riddolls
Implementation Of Method For Operating Multiple High Frequency Surface Wave Radars On A Common Carrier Frequency, Ryan Riddolls
Turkish Journal of Electrical Engineering and Computer Sciences
The increasing use of High Frequency Surface Wave Radar (HFSWR) for the surveillance of coastal regions is faced with the problem of limited channel availability in the electromagnetic spectrum. Thus, there is a need for multiple radars to share a common frequency channel. Proof-of-concept work is presented here for a method to operate multiple radar systems on a common carrier frequency. A review is provided of an existing concept where a common waveform is modulated by tones varying by a few hertz across the different radars. The signals from the different radars are separated by either pulse-domain filtering or Doppler …
Securing Fuzzy Vault Schemes Through Biometric Hashing, Cengi̇z Örenci̇k, Thomas Brochmann Pedersen, Erkay Savaş, Mehmet Keski̇nöz
Securing Fuzzy Vault Schemes Through Biometric Hashing, Cengi̇z Örenci̇k, Thomas Brochmann Pedersen, Erkay Savaş, Mehmet Keski̇nöz
Turkish Journal of Electrical Engineering and Computer Sciences
The fuzzy vault scheme is a well-known technique to mitigate privacy, security, and usability related problems in biometric identification applications. The basic idea is to hide biometric data along with secret information amongst randomly selected chaff points during the enrollment process. Only the owner of the biometric data who presents correct biometrics can recover the secret and identify himself. Recent research, however, has shown that the scheme is vulnerable to certain types of attacks. The recently proposed ``correlation attack'', that allows linking two vaults of the same biometric, pose serious privacy risks that have not been sufficiently addressed. The primary …
Corrective Action Planning Considering Facts Allocation And Optimal Load Shedding Using Bacterial Foraging Oriented By Particle Swarm Optimization Algorithm, Rahmat Allah Hooshmand, Mostafa Ezatabadi
Corrective Action Planning Considering Facts Allocation And Optimal Load Shedding Using Bacterial Foraging Oriented By Particle Swarm Optimization Algorithm, Rahmat Allah Hooshmand, Mostafa Ezatabadi
Turkish Journal of Electrical Engineering and Computer Sciences
Reactive power planning (RPP) involves optimal allocation and determination of the type and size of new reactive power (VAR) supplies to satisfy voltage constraints during normal and contingency states. The RPP issue is in fact an optimization of large scale mixed integer nonlinear programming problem, so it is proper to use an evolutionary algorithm to solve the problem. In this paper, in order to solve the RPP problem for corrective action of power systems, the bacterial foraging (BF) oriented by particle swarm optimization (PSO) algorithm (BF-PSO) is proposed. In the algorithm, the VAR control has been carried out by using …
Adaptive Neuro-Fuzzy Inference System To Improve The Power Quality Of Variable-Speed Wind Power Generation System, Yüksel Oğuz, Kami̇l Ri̇fat İrfan Güney
Adaptive Neuro-Fuzzy Inference System To Improve The Power Quality Of Variable-Speed Wind Power Generation System, Yüksel Oğuz, Kami̇l Ri̇fat İrfan Güney
Turkish Journal of Electrical Engineering and Computer Sciences
In this study, an adaptive neuro-fuzzy inference system is designed for output voltage and frequency control of a variable-speed wind power generation system. Variable-speed wind power generation systems (VSWPGS) provide the opportunity to capture more power than fixed speed turbines. On the other hand, the variable-speed wind turbine output can be variable voltage and variable frequency for fluctuating wind speeds. The quality of output power can be improved if adequate controls are incorporated in the system. To bring the output voltage and frequency of system by means of control of blade pitch angle of wind turbine to a desirable value, …
The Analysis Of A Semiconductor Single Asymmetric And Symmetric Step-Index Laser For Even And Odd Fields By Alpha Method, Mustafa Temi̇z, Mehmet Ünal
The Analysis Of A Semiconductor Single Asymmetric And Symmetric Step-Index Laser For Even And Odd Fields By Alpha Method, Mustafa Temi̇z, Mehmet Ünal
Turkish Journal of Electrical Engineering and Computer Sciences
In this work, semiconductor step-index single waveguide has been analyzed by Alpha Method. A requested quantity of wave guide can be obtained in terms of normalized propagation constant, which is represented by alpha belonging to active region. Based on this method, structural properties of the material containing any requested quantity of the waveguide is theoretically calculated, when the width of the active region, the refractive indices of the regions and the wavelength are given. In the TE mode some important parameters, such as the propagation constants for regions of the semiconductor step-index single waveguide, the wave numbers, the effective index …
Fractional Order Sliding Mode Control With Reaching Law Approach, Mehmet Önder Efe
Fractional Order Sliding Mode Control With Reaching Law Approach, Mehmet Önder Efe
Turkish Journal of Electrical Engineering and Computer Sciences
Fractional order sliding mode control is studied in this paper. The control objectives are achieved by adopting the reaching law approach of sliding mode control. The main contribution of this work is to show that the philosophy of integer order sliding mode control is valid also for the systems represented by fractional order operators. A sufficient condition and its implications for stability are given. Matched and unmatched uncertainties are studied. The attractor nature of the switching manifold is analyzed together with a stable sliding subspace design condition. The claims are justified through a set of simulations and the results obtained …
A Novel Algorithm For Sensorless Motion Control Of Flexible Structures, Islam Shoukry Mohammed Khalil, Emrah Deni̇z Kunt, Asif Sabanovic
A Novel Algorithm For Sensorless Motion Control Of Flexible Structures, Islam Shoukry Mohammed Khalil, Emrah Deni̇z Kunt, Asif Sabanovic
Turkish Journal of Electrical Engineering and Computer Sciences
This article demonstrates the validity of using an actuator as a single platform for measurements during a motion control assignment of flexible systems kept free from any kind of measurement. System acceleration level dynamics, parameters and interaction forces with the environment are coupled in an incident reaction torque that naturally rises when a flexible system is subjected to an action imposed by an attached actuator to the system. This work attempts to decouple each of the system parameters out of the incident coupled reaction torque at the interface point of the actuator with the flexible system by way of measurements …
Modeling And Control Of Flow Problems By Adaptation-Based Linear Parameter Varying Models, Coşku Kasnakoğlu
Modeling And Control Of Flow Problems By Adaptation-Based Linear Parameter Varying Models, Coşku Kasnakoğlu
Turkish Journal of Electrical Engineering and Computer Sciences
In this paper a systematic modeling and control approach for flow problems is considered. A nonlinear Galerkin model is obtained from the partial differential equations (PDEs) describing the flow; and a Linear Parameter Varying (LPV) model is constructed to approximate the Galerkin model, where the parameter variation of the LPV model is controller by an adaptation mechanism. The LPV model is then treated as a surrogate on which the control design is carried out, where the parameter variations provide a range of uncertainty in which the control design must perform satisfactorily. It is shown that if certain conditions are met, …