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Stabilization of networked control systems with nonuniform random sampling periods. (English) Zbl 1214.93093

Summary: A new linear delayed delta operator switched system model is proposed to describe networked control systems with packets dropout and network-induced delays. The plant is a continuous-time system, which is sampled by time-varying random sampling periods. A general delta domain Lyapunov stability criterion is given for delta operator switched systems with time delays. Sufficient conditions for asymptotic stability of closed-loop networked control systems with both packets dropout and network-induced delays are presented in terms of Linear Matrix Inequalities (LMIs). A verification theorem is given to show the solvability of the stabilization conditions by solving a class of finite LMIs. Both the case of data packets arrive instantly and the case of invariant sampling periods in delta operator systems are given, respectively. Three numerical examples are given to illustrate the effectiveness and potential of the developed techniques.

MSC:

93D20 Asymptotic stability in control theory
93D30 Lyapunov and storage functions
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93C57 Sampled-data control/observation systems
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
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