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Probability-guaranteed ${H}_{\infty }$ finite-horizon filtering for a class of nonlinear time-varying systems with sensor saturations. (English) Zbl 1250.93121
Summary: In this paper, the probability-guaranteed ${H}_{\infty }$ finite-horizon filtering problem is investigated for a class of nonlinear time-varying systems with uncertain parameters and sensor saturations. The system matrices are functions of mutually independent stochastic variables that obey uniform distributions over known finite ranges. Attention is focused on the construction of a time-varying filter such that the prescribed ${H}_{\infty }$ performance requirement can be guaranteed with probability constraint. By using the Difference Linear Matrix Inequalities (DLMIs) approach, sufficient conditions are established to guarantee the desired performance of the designed finite-horizon filter. The time-varying filter gains can be obtained in terms of the feasible solutions of a set of DLMIs that can be recursively solved by using the semi-definite programming method. A computational algorithm is specifically developed for the addressed probability-guaranteed ${H}_{\infty }$ finite-horizon filtering problem. Finally, a simulation example is given to illustrate the effectiveness of the proposed filtering scheme.
##### MSC:
 93E11 Filtering in stochastic control 93B36 ${H}^{\infty }$-control 93C10 Nonlinear control systems