scholarly journals Sufficient Conditions for Robust Stability of Linear Systems with Both Time-Varying Delay and Uncertainties

1996 ◽  
Vol 32 (1) ◽  
pp. 8-15
Author(s):  
Hansheng WU ◽  
Koichi MIZUKAMI
Keyword(s):  
Linear Systems ◽  
Robust Stability ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Time Varying Delay ◽  
Varying Delay

Exponential Stability for Grey Linear Systems with Time-Varying Delay

2013 ◽  
Vol 760-762 ◽  
pp. 2258-2262
Author(s):  
Ji Chao Wang ◽  
Li Jun Song ◽  
Wei Liu ◽  
Jin Fang Han
Keyword(s):  
Exponential Stability ◽  
Linear Systems ◽  
Stability Problem ◽  
Measure Theory ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Matrix Measure ◽  
Time Varying Delay ◽  
The Matrix ◽  
Varying Delay

In this paper, the exponential stability problem of grey linear systems with time-varying delay is investigated. By using the matrix measure theory and differential inequality approach, some practical sufficient conditions for guaranteeing the exponential stability of the grey linear systems with time-varying delay are presented. The grey-matrix measure and norm are also introduced.

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 Finite-Time Boundedness Analysis for a Class of Switched Linear Systems with Time-Varying Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Yanke Zhong ◽  
Tefang Chen
Keyword(s):  
Linear Systems ◽  
Finite Time ◽  
External Disturbance ◽  
Sufficient Conditions ◽  
Jensen Inequality ◽  
Time Varying ◽  
Switched Linear Systems ◽  
Time Varying Delay ◽  
Finite Time Boundedness ◽  
Varying Delay

The problem of finite-time boundedness for a class of switched linear systems with time-varying delay and external disturbance is investigated. First of all, the multiply Lyapunov function of the system is constructed. Then, based on the Jensen inequality approach and the average dwell time method, the sufficient conditions which guarantee the system is finite-time bounded are given. Finally, an example is employed to verify the validity of the proposed method.

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