Abstract
This paper provides the stochastic finite-time stabilization and H∞ control problem of Mar- kov jump systems with norm-bounded uncertainties and state delays that possess randomly jumping parameters. The transition of the jumping parameters is governed by a finite-state Markov process. The finite-time H∞ controller via state feedback is provided to guarantee the stochastic finite-time bounded- ness and stochastic finite-time stabilization of the resulting closed-loop system for all admissible un- certainties and unknown time-delays. 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. Simulation results illustrate the effectiveness of the developed approaches.
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