## A delay-partitioning approach to the stability analysis of discrete-time systems.(English)Zbl 1194.93131

Summary: This paper revisits the problem of stability analysis for linear discrete-time systems with time-varying delay in the state. By utilizing the delay partitioning idea, new stability criteria are proposed in terms of linear matrix inequalities (LMIs). These conditions are developed based on a novel Lyapunov functional. In addition to delay dependence, the obtained conditions are also dependent on the partitioning size. We have also established that the conservatism of the conditions is a non-increasing function of the number of partitions. Numerical examples are given to illustrate the effectiveness and advantage of the proposed methods.

### MSC:

 93C55 Discrete-time control/observation systems 93D20 Asymptotic stability in control theory

### Keywords:

asymptotic stability; discrete-time systems; delay systems
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### References:

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