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Exact Upper And Lower Bounds Of Crossing Frequency Set And Delay Independent Stability Test For Multiple Time Delayed Systems, Ismail Ilker Delice, Rifat Sipahi
Exact Upper And Lower Bounds Of Crossing Frequency Set And Delay Independent Stability Test For Multiple Time Delayed Systems, Ismail Ilker Delice, Rifat Sipahi
Rifat Sipahi
A general class of linear time invariant (LTI) multiple time-delay system is investigated in order to (i) obtain exact lower and upper bounds of crossing frequency set (CFS), and (ii) test the necessary and sufficient conditions of delay independent stability (DIS). The method commences by deploying Rekasius substitution for the transcendental terms in the characteristic function, reducing it into a finite dimensional one. After substitution, utilization of elimination theory allows one to achieve the two nontrivial objectives (i)-(ii). The approach is new and novel as it does not require any parameter sweeping and graphical display; it is exact and can …
Controller Design For Delay-Independent Stability Of Multiple Time-Delay Systems Via Déscartes's Rule Of Signs, Ismail Ilker Delice, Rifat Sipahi
Controller Design For Delay-Independent Stability Of Multiple Time-Delay Systems Via Déscartes's Rule Of Signs, Ismail Ilker Delice, Rifat Sipahi
Rifat Sipahi
A general class of multi-input linear time-invariant (LTI) multiple time-delay system (MTDS) is investigated in order to obtain a control law which stabilizes the LTI-MTDS independently of all the delays. The method commences by reformulating the infinite-dimensional analysis as a finite-dimensional algebraic one without any sacrifice of accuracy and exactness. After this step, iterated discriminant allows one to construct a single-variable polynomial, coefficients of which are the controller gains. This crucial step succinctly formulates the delay-independent stability (DIS) condition of the controlled MTDS based on the roots of the single-variable polynomial. Implementation of the Déscartes's rule of signs then reveals, …
Exact Stability Analysis Of Neutral Systems With Cross-Talking Delays, Nejat Olgac, Tomáš Vyhlídal, Rifat Sipahi
Exact Stability Analysis Of Neutral Systems With Cross-Talking Delays, Nejat Olgac, Tomáš Vyhlídal, Rifat Sipahi
Rifat Sipahi
The stability of neutral systems with two cross-talking delays is investigated using the method of cluster treatment of characteristic roots (CTCR). here are two main outcomes of this study: (a) Generation of the well-known delay stabilizability condition as a by-product of the CTCR procedure. This is achieved by a small delay stability treatment over the system. We also demonstrate for the delay-stabilizable systems the exact bounds of the stability regions in the domain of the delays. (b) Validation of these stability regions using an alternative point-wise algorithm, which computes the right-most roots of the characteristic quasi-polynomial.
Analytical Stability Study Of A Deterministic Car Following Model Under Multiple Delay Interactions, Rifat Sipahi, Silviu-Iulian Niculescu
Analytical Stability Study Of A Deterministic Car Following Model Under Multiple Delay Interactions, Rifat Sipahi, Silviu-Iulian Niculescu
Rifat Sipahi
Analytical stability study of some deterministic car following models under time-delay influences is presented and various case studies are demonstrated. Interestingly, for some control law deployed by human drivers, more than one stability interval in the domain of time delay is revealed. Physical interpretations along with comparisons conclude the study.
A Comparative Survey In Determining The Imaginary Characteristic Roots Of Lti Time Delayed Systems, Rifat Sipahi, Nejat Olgac
A Comparative Survey In Determining The Imaginary Characteristic Roots Of Lti Time Delayed Systems, Rifat Sipahi, Nejat Olgac
Rifat Sipahi
The aim of this study is to offer a comparison of the numerical procedures for an important problem, the determination of purely imaginary characteristic roots of LTITime Delayed Systems (LTI-TDS). This problem, in fact, has a crucial role in assessing the stability of the general class of vector LTI-TDS x = Ax + Bx(t -τ). There are many procedures discussed in the literature for this purpose. Those, which are exact, first determine the complete set of imaginary characteristic roots of the dynamics, as they constitute the only points where stability switching can take place. These approaches are, in fact, some …
A New Perspective In The Stability Assessment Of Neutral Systems With Multiple And Cross-Talking Delays, Nejat Olgac, Tomáš Vyhlídal, Rifat Sipahi
A New Perspective In The Stability Assessment Of Neutral Systems With Multiple And Cross-Talking Delays, Nejat Olgac, Tomáš Vyhlídal, Rifat Sipahi
Rifat Sipahi
The stability of neutral systems with two cross-talking delays is investigated using the method of cluster treatment of characteristic roots (CTCR). There are two main outcomes of this study: (a) we create the “strong stabilizability” (also called the “delay stabilizability”) of the system directly from the CTCR procedure. This is achieved by a small-delay stability treatment while performing the steps of the CTCR. For the “delay-stabilizable systems,” we also arrive at the exact bounds of the stability regions in the domain of the delays. (b) We deploy a point-wise algorithm which computes the rightmost roots of the characteristic quasi polynomial …
Complete Stability Map Of First Order - Two Time Delay Systems With Delay Cross-Talk, Rifat Sipahi, Nejat Olgac
Complete Stability Map Of First Order - Two Time Delay Systems With Delay Cross-Talk, Rifat Sipahi, Nejat Olgac
Rifat Sipahi
First order linear time invariant dynamics is taken into account with two delays. A unique feature is included in this study, from the stability perspective: a term that represents the cross-talk between the two delays. This class of systems can be treated by a unique procedure, which is recently developed, known as Cluster Treatment of Characteristic Roots (CTCR). In the text we present several case studies to display the steps and the strengths of CTCR. We also include some comparison results with respect to a cornerstone study (Hale, and Huang, 1993), which gives a wonderful point of reference for this …
Stability Robustness Of Retarded Lti Systems With Single Delay And Exhaustive Determination Of Their Imaginary Spectra, Rifat Sipahi, Nejat Olgac
Stability Robustness Of Retarded Lti Systems With Single Delay And Exhaustive Determination Of Their Imaginary Spectra, Rifat Sipahi, Nejat Olgac
Rifat Sipahi
In this paper we consider the stability robustness of the general class of vector LTI (linear time invariant) equations with a single delay, $\dot{\bf x}(t) = {\bf A}{\bf x}(t) + {\bf B}{\bf x}(t-\tau)$, ${\bf x} \in {\bf R}^n$. The robustness is against the uncertain, but constant delay, $\tau \in {\bf R}^+$. We first present a set of novel propositions and state that the solution must start from the complete knowledge of imaginary spectra of the system, and the corresponding delays. The propositions claim that such spectra form a set of manageably small number of members, and this number is upper …
Supply Network Dynamics And Delays; Performance, Synchronization, Stability, Rifat Sipahi, Ismail Ilker Delice
Supply Network Dynamics And Delays; Performance, Synchronization, Stability, Rifat Sipahi, Ismail Ilker Delice
Rifat Sipahi
Recent research results in operations research specifically emphasize the critical role of delays in the functionality of supply networks. Delays arise due to the time needed for material deliveries, information flow and human perception towards adjusting to new decisions. Delays contaminate decision-making and lead to poor performance, synchronization problems and fluctuations in inventory levels resulting in major economical losses. This paper surveys continuous time deterministic mathematical models developed at system-level for supply network dynamics along with standard delay models pertaining to material deliveries, information flows and human perception. Next, the analogy between such delay models arising in supply networks and …
Complete Stability Analysis Of Neutral‐Type First Order Two‐Time‐Delay Systems With Cross‐Talking Delays, Rifat Sipahi, Nejat Olgac
Complete Stability Analysis Of Neutral‐Type First Order Two‐Time‐Delay Systems With Cross‐Talking Delays, Rifat Sipahi, Nejat Olgac
Rifat Sipahi
The stability robustness of first order linear time invariant dynamics of neutral type with multiple time delays against delay uncertainties is taken into consideration. We depart from a simpler investigation of Hale and Huang [J. Math. Anal. Appl., 178 (1993), pp. 344–362], which studies the same problem for retarded‐type systems. On this basis we further introduce two challenging features by including (a) terms that add neutral dynamics and (b) an additional term that introduces cross‐talk between the multiple delays. To the best of the authors’ knowledge, the stability posture of this class of systems can be treated only by a …