## Observer-based finite-time $$H_\infty$$ control of discrete-time Markovian jump systems.(English)Zbl 1270.93046

Summary: This paper investigates the observer-based finite-time $$H_\infty$$ control problem for one family of discrete-time Markovian jump systems with time-varying norm-bounded disturbance. Firstly, the concepts of stochastic finite-time boundedness and stochastic $$H_\infty$$ finite-time stabilization via observer-based state feedback are given. Then, under the assumption that the state vector is not available for feedback, an observer-based state feedback controller is designed to ensure stochastic finite-time stabilization or stochastic $$H_\infty$$ finite-time stabilization via observer-based state feedback of the resulting closed-loop error discrete-time Markovian jump system. Sufficient criteria on the stochastic finite-time stabilization and stochastic $$H_\infty$$ finite-time stabilization via observer-based state feedback are given in form of linear matrix inequalities with a fixed parameter, respectively. Finally, simulation examples are presented to illustrate the validity of the developed techniques.

### MSC:

 93B36 $$H^\infty$$-control 93E15 Stochastic stability in control theory
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### References:

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