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Delay-distribution-dependent robust stability of uncertain systems with time-varying delay. (English) Zbl 1157.93478

Summary: By employing the information of the probability distribution of the time delay, this paper investigates the problem of robust stability for uncertain systems with time-varying delay satisfying some probabilistic properties. Different from the common assumptions on the time delay in the existing literatures, it is assumed in this paper that the delay is random and its probability distribution is known a priori. In terms of the probability distribution of the delay, a new type of system model with stochastic parameter matrices is proposed. Based on the new system model, sufficient conditions for the exponential mean square stability of the original system are derived by using the Lyapunov functional method and the Linear Matrix Inequality (LMI) technique. The derived criteria, which are expressed in terms of a set of LMIs, are delay-distribution-dependent, that is, the solvability of the criteria depends on not only the variation range of the delay but also the probability distribution of it. Finally, three numerical examples are given to illustrate the feasibility and effectiveness of the proposed method.

MSC:

93D09 Robust stability
93E03 Stochastic systems in control theory (general)
93C15 Control/observation systems governed by ordinary differential equations
34K50 Stochastic functional-differential equations
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