The stochastic finite-time stabilization problem is considered for a class of linear uncertain Markov jump systems that possess randomly jumping parameters. The transition of the jumping parameters is governed by a finite-state Markov process. By using the appropriate stochastic Lyapunov–Krasovskii functional approach, sufficient conditions are proposed for the design of stochastic finite-time stabilization controller. The stabilization criteria are formulated in the form of linear matrix inequalities and the designed finite-time stabilization controller is described as an optimization one. The designed finite-time stabilized controller makes the stochastic MJSs stochastic finite-time bounded and stochastic finite-time stabilizable for all admissible unknown external disturbances and uncertain parameters. Simulation results illustrate the effectiveness of the developed approaches.

Issue Section:
Technical Briefs
Keywords:
linear matrix inequalities, Lyapunov methods, Markov processes, robust control, state feedback, Markov jump systems (MJSs), stochastic finite-time stabilization, stochastic finite-time bounded, uncertain, linear matrix inequalities
Topics:
Control equipment, Linear matrix inequalities, Markov processes, Optimization, State feedback, Design
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