scholarly journals A Panoramic Sketch about the Robust Stability of Time-Delay Systems and Its Applications

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-26
Author(s):  
Baltazar Aguirre-Hernández ◽  
Raúl Villafuerte-Segura ◽  
Alberto Luviano-Juárez ◽  
Carlos Arturo Loredo-Villalobos ◽  
Edgar Cristian Díaz-González
Keyword(s):  
Time Delay ◽  
Dynamical Systems ◽  
Robust Stability ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Complex Dynamical Systems ◽  
The Stability ◽  
Numerical Approaches

This paper presents a brief review on the current applications and perspectives on the stability of complex dynamical systems, with an emphasis on three main classes of systems such as delay-free systems, time-delay systems, and systems with uncertainties in its parameters, which lead to some criteria with necessary and/or sufficient conditions to determine stability and/or stabilization in the domains of frequency and time. Besides, criteria on robust stability and stability of nonlinear time-delay systems are presented, including some numerical approaches.

scholarly journals Robust stability of linear perturbed discrete systems with multiple time-delay

2006 ◽  
Vol 60 (3-4) ◽  
pp. 82-86
Author(s):  
Sreten Stojanovic ◽  
Dragutin Debeljkovic ◽  
Ilija Mladenovic
Keyword(s):  
Time Delay ◽  
Asymptotic Stability ◽  
Robust Stability ◽  
Sufficient Conditions ◽  
Discrete Systems ◽  
Numerical Results ◽  
Delay Systems ◽  
Multiple Delays ◽  
Multiple Time ◽  
Time Delay Systems

The paper presents some new sufficient conditions, independent of delay, for the asymptotic stability of a particular class of linear perturbed time-delay systems with multiple delays. The proposed criteria introduce a smaller number of assumptions and are expressed in more natural and simpler mathematical forms. Numerical results are presented to support and illustrate the derived results.

Robust Stabilizability of Uncertain Linear Time-Delay Systems With Markovian Jumping Parameters

1996 ◽  
Vol 118 (4) ◽  
pp. 776-783 ◽  
Author(s):  
K. Benjelloun ◽  
E. K. Boukas ◽  
H. Yang
Keyword(s):  
Time Delay ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Markovian Jumping Parameters ◽  
Markovian Jumping ◽  
Linear Type ◽  
Continuous State ◽  
The Stability

In this paper, we deal with the robust stabilizability of the class of uncertain linear time-delay systems with Markovian jumping parameters and unknown but bounded uncertainties. Under the assumption of the complete access to the continuous state, the stochastic controllability of the nominal system and the boundedness of the system’s uncertainties, sufficient conditions which guarantee the robustness of the stability of this class of systems are given. The control law which guarantees the robustness of the stabilizability is linear-type or saturation-type. An example is presented to illustrate the usefulness of the proposed theoretical results.

Robust Regional Eigenvalue-Clustering Analysis for Linear Discrete Singular Time-Delay Systems With Structured Parameter Uncertainties

2006 ◽  
Vol 129 (1) ◽  
pp. 83-90 ◽  
Author(s):  
Shinn-Horng Chen ◽  
Jyh-Horng Chou ◽  
Liang-An Zheng
Keyword(s):  
Time Delay ◽  
Sufficient Conditions ◽  
Delay System ◽  
Delay Systems ◽  
Sufficient Condition ◽  
Time Delay Systems ◽  
Parameter Uncertainties ◽  
Time Delay System ◽  
The Stability ◽  
Singular Time

In this paper, the regional eigenvalue-clustering robustness problem of linear discrete singular time-delay systems with structured (elemental) parameter uncertainties is investigated. Under the assumptions that the linear nominal discrete singular time-delay system is regular and causal, and has all its finite eigenvalues lying inside certain specified regions, two new sufficient conditions are proposed to preserve the assumed properties when the structured parameter uncertainties are added into the linear nominal discrete singular time-delay system. When all the finite eigenvalues are just required to locate inside the unit circle, the proposed criteria will become the stability robustness criteria. For the case of eigenvalue clustering in a specified circular region, one proposed sufficient condition is mathematically proved to be less conservative than those reported very recently in the literature. Another new sufficient condition is also proposed for guaranteeing that the linear discrete singular time-delay system with both structured (elemental) and unstructured (norm-bounded) parameter uncertainties holds the properties of regularity, causality, and eigenvalue clustering in a specified region. An example is given to demonstrate the applicability of the proposed sufficient conditions.

CHAOS SYNCHRONIZATION OF CHEN SYSTEMS WITH TIME-VARYING DELAYS

2012 ◽  
Vol 22 (08) ◽  
pp. 1250183 ◽  
Author(s):  
JIANENG TANG ◽  
CAIRONG ZOU ◽  
SHAOPING WANG ◽  
LI ZHAO ◽  
PINGXIANG LIU
Keyword(s):  
Time Delay ◽  
Dynamical Systems ◽  
Numerical Simulations ◽  
Stability Theory ◽  
Chaos Synchronization ◽  
Delay Systems ◽  
Time Varying ◽  
Time Delay Systems ◽  
Synchronization Problem ◽  
The Stability

In this paper, the synchronization problem of Chen systems with time-varying delays is discussed based on the stability theory of time-delay systems. Through the analysis of the error dynamical systems, the time-delay correlative synchronization controller is designed to achieve chaos synchronization. And finally, numerical simulations are provided to verify the effectiveness and feasibility of the developed method.

Determination of the Tolerable Sector of Series Nonlinearities in Uncertain Time-Delay Systems Under Dynamical Output Feedback

1991 ◽  
Vol 113 (3) ◽  
pp. 525-531 ◽  
Author(s):  
Feng-Hsiag Hsiao ◽  
Jer-Guang Hsieh ◽  
Min-Sheng Wu
Keyword(s):  
Time Delay ◽  
Robust Stability ◽  
Output Feedback ◽  
Sufficient Conditions ◽  
Feedback System ◽  
Delay System ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Matrix Measure ◽  
Uncertain Time

Several sufficient conditions which guarantee robust stability of uncertain time-delay systems under dynamical output feedback with a class of series nonlinearities are derived in the time domain. Each of these results is expressed by a succinct scalar inequality and corresponds to a certain extent to the tradeoff between simplicity and sharpness. Properties of the matrix measure and the comparison theorem are employed to give robustness conditions which assure asymptotic stability rather than ultimate boundedness of trajectories. Moreover, for each uncertain time-delay system, a class of series nonlinearities lying in the sector [α, β] are found such that the overall feedback system with these nonlinearities is still asymptotically stable. An algorithm based on these robust stabilization criteria is presented to determine the tolerable range of series nonlinearities from the inverse viewpoint. It is shown that the plant uncertainties and nonlinearities may destabilize the system. Hence the nominal feedback system without series nonlinearities should be sufficiently stable to ensure robust stability.

Measures of Robustness for Uncertain Time-Delay Linear Systems

1995 ◽  
Vol 117 (4) ◽  
pp. 633-635 ◽  
Author(s):  
Said Oucheriah
Keyword(s):  
Time Delay ◽  
Linear Systems ◽  
Robust Stability ◽  
Salient Feature ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Lyapunov Matrix ◽  
The Stability ◽  
Uncertain Time ◽  
Delay Dependent

Several delay-dependent criteria to test the stability of time-delay systems that were proposed require solving the Lyapunov matrix equation. This can be a troublesome task and often nontrivial. In this note, a delay-dependent sufficient condition that guarantees the robust stability of linear uncertain time-delay systems is presented. The stability test criterion derived in this paper is based on induced norms and matrix measures. The salient feature of the result obtained is its simplicity and ease in testing the robust stability of uncertain time-delay linear systems.

scholarly journals Diagonal Riccati stability of a class of time-delay systems

2018 ◽  
pp. 167-173
Author(s):  
Alexander Aleksandrov ◽  
Nadezhda Kovaleva
Keyword(s):  
Complex System ◽  
Population Dynamics ◽  
Time Delay ◽  
Mechanical System ◽  
Formation Control ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Time Delay Systems ◽  
The Stability ◽  
Necessary And Sufficient

A complex system describing interaction of subsystems of the second order with delay in connections between them is studied. Necessary and sufficient conditions of the existence of a diagonal Lyapunov–Krasovskii functional for the considered system are derived. The obtained results are applied for the stability a nalysis of a mechanical system and a model of population dynamics. In addition, it is shown that they can be used in a problem of formation control.

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