scholarly journals Global Uniform Asymptotic Stability Criteria for Linear Uncertain Switched Positive Time-Varying Delay Systems with All Unstable Subsystems

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2118
Author(s):  
Thaned Rojsiraphisal ◽  
Piyapong Niamsup ◽  
Suriyon Yimnet
Keyword(s):  
Asymptotic Stability ◽  
Robust Stability ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Time Varying ◽  
Uniform Asymptotic Stability ◽  
Time Varying Delay ◽  
Unstable Subsystems ◽  
Positive Time ◽  
Varying Delay

In this paper, the problem of robust stability for a class of linear switched positive time-varying delay systems with all unstable subsystems and interval uncertainties is investigated. By establishing suitable time-scheduled multiple copositive Lyapunov-Krasovskii functionals (MCLKF) and adopting a mode-dependent dwell time (MDDT) switching strategy, new delay-dependent sufficient conditions guaranteeing global uniform asymptotic stability of the considered systems are formulated. Apart from past studies that studied switched systems with at least one stable subsystem, in the present study, the MDDT switching technique has been applied to ensure robust stability of the considered systems with all unstable subsystems. Compared with the existing results, our results are more general and less conservative than some of the previous studies. Two numerical examples are provided to illustrate the effectiveness of the proposed methods.

scholarly journals Input–output linearization of non-linear time-varying delay systems: the single-input single-output case

2019 ◽  
Vol 37 (3) ◽  
pp. 831-854
Author(s):  
Ihab Haidar ◽  
Florentina Nicolau ◽  
Jean-Pierre Barbot ◽  
Woihida Aggoune
Keyword(s):  
Linear Time ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Time Varying ◽  
Input Output ◽  
Time Varying Delay ◽  
Output Stabilization ◽  
Non Linear ◽  
Varying Delay ◽  
Input Output Linearization

Abstract This paper deals with the input–output linearization of non-linear time-varying delay systems. We introduce an extension of the Lie derivative for time-varying delay systems and derive sufficient conditions for the existence of a causal and bounded non-linear feedback linearizing the input–output behaviour of the system. Sufficient conditions ensuring the internal stability after output stabilization are also presented. Finally, several examples illustrating our main results are discussed.

scholarly journals Robust Stability of Time-Varying Delay Systems: The Quadratic Separation Approach

2012 ◽  
Vol 14 (5) ◽  
pp. 1205-1214 ◽  
Author(s):  
Yassine Ariba ◽  
Frédéric Gouaisbaut ◽  
Karl Henrik Johansson
Keyword(s):  
Robust Stability ◽  
Delay Systems ◽  
Time Varying ◽  
Time Varying Delay ◽  
Varying Delay

State feedback stabilization of linear descriptor time-varying delay systems

2020 ◽  
Vol 42 (12) ◽  
pp. 2191-2197 ◽  
Author(s):  
Piyapong Niamsup ◽  
Vu N Phat
Keyword(s):  
State Feedback ◽  
Sufficient Conditions ◽  
Feedback Stabilization ◽  
Descriptor Systems ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Delay Function ◽  
Time Varying Delay ◽  
Varying Delay

In this paper, the augmented Lyapunov-Krasovskii function approach combining with singular value decomposition method is developed for stabilization of linear descriptor systems with time-varying delay. The delay function is non-differentiable, but continuous and bounded. By introducing a set of improved Lyapunov-Krasovskii functionals we propose delay-dependent sufficient conditions for admissibility of the system in terms of linear matrix inequalities. Then, based on the obtained stability results the problem of stabilization is solved via state feedback controllers, which guarantees that the descriptor closed-loop system is admissible. An numerical example with simulation is provided to show the effectiveness of the theoretical result.

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