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Finite-horizon $\cal H_{2}/\cal H_{\infty }$ control for a class of nonlinear Markovian jump systems with probabilistic sensor failures. (English) Zbl 1236.93052
Summary: This article is concerned with the mixed $\cal H_{2}/\cal H_{\infty }$ control problem over a finite horizon for a class of nonlinear Markovian jump systems with both stochastic nonlinearities and probabilistic sensor failures. The stochastic nonlinearities described by statistical means could cover several types of well-studied nonlinearities, and the failure probability for each sensor is governed by an individual random variable satisfying a certain probability distribution over a given interval. The purpose of the addressed problem is to design state feedback controllers such that the closed-loop system achieves the expected $\cal H_{2}$ performance requirement with a guaranteed $\cal H_{\infty }$ disturbance attenuation level. The solvability of the addressed control problem is expressed as the feasibility of certain coupled matrix equations. The controller gain at each time instant $k$ can be obtained by solving the corresponding set of matrix equations. A numerical example is given to illustrate the effectiveness and applicability of the proposed algorithm.

MSC:
93B36$H^\infty$-control
60J75Jump processes
93C10Nonlinear control systems
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