# Operations Research, Systems Engineering and Industrial Engineering Commons™

Articles 1 - 8 of 8

## Full-Text Articles in Operations Research, Systems Engineering and Industrial Engineering

Rules And Limitations Of Building Delay-Tolerant Topologies For Coupled Systems, Rifat Sipahi, Wei Qiao Apr 2012

#### Rules And Limitations Of Building Delay-Tolerant Topologies For Coupled Systems, Rifat Sipahi, Wei Qiao

##### Rifat Sipahi

This paper investigates the equilibrium behavior of broadly studied synchronization dynamics of coupled systems, among which shared information is delayed. The underlying relationship is established between graph structures and the largest amount of delay the dynamics can withstand without losing stability. In particular, based on Cartesian product of graphs, we present the rules and limitations for synthesizing the graphs of large-scale systems that can remain stable for as large delays as possible. Examples are provided to demonstrate the results.

Exact Stability Analysis Of Neutral Systems With Cross-Talking Delays, Nejat Olgac, Tomáš Vyhlídal, Rifat Sipahi Apr 2012

#### 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 Apr 2012

#### 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 Apr 2012

#### 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 variations ...

Complete Stability Map Of First Order - Two Time Delay Systems With Delay Cross-Talk, Rifat Sipahi, Nejat Olgac Apr 2012

#### 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 ...

Apr 2012

#### 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 ...

Complete Stability Analysis Of Neutral‐Type First Order Two‐Time‐Delay Systems With Cross‐Talking Delays, Rifat Sipahi, Nejat Olgac Apr 2012

#### 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 ...

#### Cluster Treatment Of Characteristic Roots, Ctcr, A Unique Methodology For The Complete Robustness Analysis Of Linear Time Invariant Multiple Time Delay Systems Against Delay Uncertainties, Rifat Sipahi

##### Rifat Sipahi

Today, many high-tech applications such as simultaneous metal machining, neural networks, internet data congestion, population dynamics, chemical processes, formation flight problems, etc., appear in the form of multiple time delay systems (MTDS ). Due to the presence of delays, the stability of the dynamics is under question and needs to be addressed. In the last four decades, the stability analysis of the general class, Linear Time Invariant MTDS (LTI-MTDS), has been one of the challenging problems of the systems and control community, which originates from the complex stability analysis due to their infinite dimensionality. For tackling this, a unique procedure is ...