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${H}_{\infty }$ filtering for uncertain time-varying systems with multiple randomly occurred nonlinearities and successive packet dropouts. (English) Zbl 1227.93115
Summary: This paper is concerned with the robust ${H}_{\infty }$ finite-horizon filtering problem for discrete time-varying stochastic systems with Multiple Randomly Occurred Sector-Nonlinearities (MROSNs) and successive packet dropouts. MROSNs are proposed to model a class of sector-like nonlinearities that occur according to the multiple Bernoulli distributed white sequences with a known conditional probability. Different from traditional approaches, in this paper, a time-varying filter is designed directly for the addressed system without resorting to the augmentation of system states and measurement, which helps reduce the filter order. A new ${H}_{\infty }$ filtering technique is developed by means of a set of recursive linear matrix inequalities that depend not only on the current available state estimate but also on the previous measurement. Finally, two illustrative examples are used to demonstrate the effectiveness and applicability of the proposed filter design scheme.
##### MSC:
 93E10 Estimation and detection in stochastic control 93B36 ${H}^{\infty }$-control 93C10 Nonlinear control systems