A piecewise analysis method to stability analysis of linear continuous/discrete systems with time-varying delay

2009 ◽  
Vol 19 (13) ◽  
pp. 1493-1518 ◽  
Author(s):  
Dong Yue ◽  
Engang Tian ◽  
Yijun Zhang
Keyword(s):  
Stability Analysis ◽  
Discrete Systems ◽  
Time Varying ◽  
Analysis Method ◽  
Time Varying Delay ◽  
Varying Delay

New Stability Condition for Linear Systems with Time-Varying Delay

2014 ◽  
Vol 898 ◽  
pp. 843-846
Author(s):  
Li Jun Wang
Keyword(s):  
Stability Analysis ◽  
Positive Definite Matrix ◽  
Linear Matrix ◽  
Time Varying ◽  
Analysis Method ◽  
Delayed Systems ◽  
Time Varying Delay ◽  
Weighting Matrix ◽  
Delay Dependent ◽  
Varying Delay

Generally, the obtained results on delayed systems can be classified into two types: delay-independent ones and delay-dependent ones. Delay-dependent stabilization problem for a class linear system with interval time-varying delay is studied. Early first proposed stability analysis method for systems with time-varying delay in a range, but the method therein still leaves much room for improvement. A sufficient condition in terms of linear matrix inequalities (LMIs) is achieved by constructing a novel Lyapunov-Krasovskii functional with the idea of partitioning the time delay, and then using free-weighting matrix approach and adopting inequalities, the interval delay is dealt with successfully. Compared with former stability analysis approaches, this approach can overcome the defect of finding a common positive definite matrix, and reduce conservative greatly. Finally, one simulation example is given to illustrate the effectiveness of the methods.

A new control approach for a class of linear switched systems with time-varying delay

2021 ◽  
pp. 014233122199272
Author(s):  
Abbas Zabihi Zonouz ◽  
Mohammad Ali Badamchizadeh ◽  
Amir Rikhtehgar Ghiasi
Keyword(s):  
Stability Analysis ◽  
Linear Matrix Inequalities ◽  
Linear Matrix ◽  
Switching Systems ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
Linear Switching Systems ◽  
The Stability ◽  
Varying Delay

In this paper, a new method for designing controller for linear switching systems with varying delay is presented concerning the Hurwitz-Convex combination. For stability analysis the Lyapunov-Krasovskii function is used. The stability analysis results are given based on the linear matrix inequalities (LMIs), and it is possible to obtain upper delay bound that guarantees the stability of system by solving the linear matrix inequalities. Compared with the other methods, the proposed controller can be used to get a less conservative criterion and ensures the stability of linear switching systems with time-varying delay in which delay has way larger upper bound in comparison with the delay bounds that are considered in other methods. Numerical examples are given to demonstrate the effectiveness of proposed method.

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