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Stochastic $\cal H_\infty$ finite-time control of discrete-time systems with packet loss. (English) Zbl 1264.93231
Summary: This paper investigates the stochastic finite-time stabilization and $\cal H_\infty$ control problem for one family of linear discrete-time systems over networks with packet loss, parametric uncertainties, and time-varying norm-bounded disturbance. Firstly, the dynamic model description studied is given, which, if the packet dropout is assumed to be a discrete-time homogenous Markov process, the class of discrete-time linear systems with packet loss can be regarded as Markovian jump systems. Based on Lyapunov function approach, sufficient conditions are established for the resulting closed-loop discrete-time system with Markovian jumps to be stochastic $\cal H_\infty$ finite-time boundedness and then state feedback controllers are designed to guarantee stochastic $\cal H_\infty$ finite-time stabilization of the class of stochastic systems. The stochastic $\cal H_\infty$ finite-time boundedness criteria can be tackled in the form of linear matrix inequalities with a fixed parameter. As an auxiliary result, we also give sufficient conditions on the robust stochastic stabilization of the class of linear systems with packet loss. Finally, simulation examples are presented to illustrate the validity of the developed scheme.

##### MSC:
 93E03 General theory of stochastic systems 93C55 Discrete-time control systems 60J10 Markov chains (discrete-time Markov processes on discrete state spaces) 93B36 $H^\infty$-control
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