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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.

##### MSC:
 93E03 Stochastic systems in control theory (general) 93C10 Nonlinear systems in control theory 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory 93E15 Stochastic stability in control theory
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