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.

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.

Robust stability of uncertain linear systems with multiple time delays

1997 ◽  
Vol 211 (3) ◽  
pp. 195-202
Author(s):  
Y Fang
Keyword(s):  
Linear Systems ◽  
Robust Stability ◽  
Time Delays ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Multiple Time ◽  
Time Delay Systems ◽  
Multiple Time Delays ◽  
Uncertain Linear Systems

In this paper, the robust stability of uncertain linear systems with multiple time delays is studied. Sufficient conditions for robust stability of linear time delay systems with convex perturbations are obtained. From these sufficient conditions, a few results on robust stability of systems with other perturbations are derived. Some previously known sufficient conditions are generalized.

Robust Controller Design for Discrete Uncertain Multiple Time-Delay Systems

1997 ◽  
Vol 119 (1) ◽  
pp. 122-127 ◽  
Author(s):  
Feng-Hsiag Hsiao ◽  
Shing-Tai Pan ◽  
Ching-Cheng Teng
Keyword(s):  
Time Delay ◽  
Uncertain Systems ◽  
Controller Design ◽  
Delay Systems ◽  
Multiple Delays ◽  
Multiple Time ◽  
Time Delay Systems ◽  
Ultimate Boundedness ◽  
Robust Controller ◽  
Robust Controller Design

We derive a variety of succinct criteria of robust stability for discrete uncertain systems which contain multiple delays and a class of series nonlinearities. Each result is expressed by a brief inequality and corresponds to compromise between simplicity and sharpness. The properties of norm are employed to investigate robustness conditions that guarantee asymptotic stability rather than ultimate boundedness of trajectories. It is shown that the uncertainties, nonlinearities, and delays are the factors of instability of the overall system, between which some compromise is necessary.

scholarly journals On the Asymptotic Stability of Linear Discrete Time Delay Systems

Volume 1 ◽  
2004 ◽  
Author(s):  
S. B. Stojanovic ◽  
D. Lj. Debeljkovic
Keyword(s):  
Time Delay ◽  
Asymptotic Stability ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Numerical Example ◽  
Discrete Time Delay ◽  
Time Invariant ◽  
Working Out

This paper extends some of the basic results in the area of Lyapunov (asymptotic) to linear, discrete, time invariant time-delay systems. These results are given in the form of only sufficient conditions and represent other generalisation of some previous ones or completely new results. In the latter case it is easy to show that, in the most cases, these results are less conservative then those in existing literature. A numerical example has been working out to show the applicability of results derived. To the best knowledge of the authors, such results have not yet been reported.

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.

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