Non-Fragile $$H_{\infty }$$ H ∞ Filter Design for Uncertain Stochastic Nonlinear Time-Delay Markovian Jump Systems

Abstract

This paper investigates the problem of non-fragile and mode-dependent $$H_{\infty }$$ H ? filter design for a class of nonlinear stochastic Markovian jump systems with mode-dependent time-varying delays and norm-bounded parameter uncertainties. The non-fragile and mode-dependent filter to be designed is assumed to include multiplicative gain variations which result from inaccuracies in filter implementation, and the desired filter ensures the filtering error system is not only exponentially mean-square stable, but also satisfies a prescribed $$H_{\infty }$$ H ? -norm level for all admissible uncertainties. A stochastic Lyapunov---Krasovskii function is proposed to reflect the information of Markovian jump modes and the mode-dependent time-varying delays, and a set of strict linear matrix inequalities are utilized to derive sufficient conditions that guarantee the desired filter can be constructed. A numerical example and a vertical take-off and landing (VTOL) helicopter system are utilized to illustrate the effectiveness and usefulness of the main results obtained.