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A delay-dependent approach to $H_{\infty}$ filtering for stochastic delayed jumping systems with sensor non-linearities. (English) Zbl 1124.93056
Summary: A delay-dependent approach is developed to deal with the stochastic $H_{\infty}$ filtering problem for a class of Itô type stochastic time-delay jumping systems subject to both the sensor non-linearities and the exogenous non-linear disturbances. The time delays enter into the system states, the sensor non-linearities and the external non-linear disturbances. The purpose of the addressed filtering problem is to seek an $H_{\infty}$ filter such that, in the simultaneous presence of non-linear disturbances, sensor non-linearity as well as Markovian jumping parameters, the filtering error dynamics for the stochastic time-delay system is stochastically stable with a guaranteed disturbance rejection attenuation level $\gamma$. By using Itô’s differential formula and the Lyapunov stability theory, we develop a linear matrix inequality approach to derive sufficient conditions under which the desired filters exist. These conditions are dependent on the length of the time delay. We then characterize the expression of the filter parameters, and use a simulation example to demonstrate the effectiveness of the proposed results.

93E03General theory of stochastic systems
93C10Nonlinear control systems
93D05Lyapunov and other classical stabilities of control systems
93E15Stochastic stability
93D05Lyapunov and other classical stabilities of control systems
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