## Observer-based finite-time control of time-delayed jump systems.(English)Zbl 1207.93113

Summary: This paper provides the observer-based finite-time control problem of time-delayed Markov Jump Systems (MJS) that possess randomly jumping parameters. The transition of the jumping parameters is governed by a finite-state Markov process. The observer-based finite-time $$H_\infty$$ controller via state feedback is proposed to guarantee the stochastic finite-time boundedness and stochastic finite-time stabilization of the resulting closed-loop system for all admissible disturbances and unknown time-delays. Based on stochastic finite-time stability analysis, sufficient conditions that ensure stochastic robust control performance of time-delay jump systems are derived. The control criterion is formulated in the form of linear matrix inequalities and the designed finite-time stabilization controller is described as an optimization one. The presented results are extended to time-varying delayed MJSs. Simulation results illustrate the effectiveness of the developed approaches.

### MSC:

 93E15 Stochastic stability in control theory 93B35 Sensitivity (robustness) 60J75 Jump processes (MSC2010)
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### References:

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