## A piecewise analysis method to stability analysis of linear continuous/discrete systems with time-varying delay.(English)Zbl 1298.93259

Summary: The delay-dependent stability problem of linear continuous/discrete systems with time-varying delay is investigated based on a piecewise analysis method (PAM). In the method, the variation interval of the time delay is firstly divided into several subintervals. By checking the variation of the Lyapunov functional in every subinterval, some new delay-dependent stability criteria are derived. Several numerical examples show that our method can lead to much less conservative results than those in the existing references. Moreover, when the number of the divided subintervals increases, the corresponding criteria can provide an improvement on the results.

### MSC:

 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory 93D30 Lyapunov and storage functions 93C05 Linear systems in control theory

### Keywords:

linear systems; stability; Lyapunov functional; LMI
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### References:

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