\(H_{\infty}\) filtering for stochastic singular fuzzy systems with time-varying delay. (English) Zbl 1331.93206
Summary: This paper considers the \(H_{\infty}\) filtering problem for stochastic singular fuzzy systems with time-varying delay. We assume that the state and measurement are corrupted by stochastic uncertain exogenous disturbance and that the system dynamic is modeled by Ito-type stochastic differential equations. Based on an auxiliary vector and an integral inequality, a set of delay-dependent sufficient conditions is established, which ensures that the filtering error system is \(e^{\lambda t}\)-weighted integral input-to-state stable in mean (iISSiM). A fuzzy filter is designed such that the filtering error system is impulse-free, \(e^{\lambda t}\)-weighted iISSiM and the \(H_{\infty}\) attenuation level from disturbance to estimation error is below a prescribed scalar. A set of sufficient conditions for the solvability of the \(H_{\infty}\) filtering problem is obtained in terms of a new type of Lyapunov function and a set of linear matrix inequalities. Simulation examples are provided to illustrate the effectiveness of the proposed filtering approach developed in this paper.
MSC:
| 93E11 | Filtering in stochastic control theory |
| 93B36 | \(H^\infty\)-control |
| 93C42 | Fuzzy control/observation systems |
| 34K36 | Fuzzy functional-differential equations |
| 34K50 | Stochastic functional-differential equations |
| 37M05 | Simulation of dynamical systems |
| 37N35 | Dynamical systems in control |
Keywords:
stochastic singular fuzzy systems; \(H_{\infty}\) filtering; \(e^{\lambda t}\)-weighted integral input-to-state stable in mean; fuzzy filterReferences:
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