scholarly journals New Sufficient Conditions for Robust Stability of Time-Delay Systems with Structured State Space Uncertainties

1996 ◽  
Vol 32 (3) ◽  
pp. 336-344
Author(s):  
Hansheng WU ◽  
Koichi MIZUKAMI
Keyword(s):  
Time Delay ◽  
State Space ◽  
Robust Stability ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Time Delay Systems

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.

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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