Finite-time mixed H ∞ and passive filtering for Takagi–Sugeno fuzzy nonhomogeneous Markovian jump systems

This paper is concerned with the finite-time mixed H∞ and passivity performance analysis and filter design for a class of uncertain nonlinear discrete-time Markovian jump systems (MJSs) described by Takagi–Sugeno fuzzy model with nonhomogeneous jump processes. In this paper, the proposed MJSs fuzzy model is formulated with norm-bounded parameter uncertainties and time-varying jump transition probability matrices. In particular, the time-varying transition probability matrices are expressed in respect of a polytope. By constructing a suitable Lyapunov functional, a new set of sufficient conditions is derived in the form of linear matrix inequalities (LMIs) to ensure that the filtering error system is robustly stochastically finite-time bounded and a prescribed mixed H∞ and passive performance index is achieved. Moreover, the robust mixed H∞ and passivity filter design gain matrices can be computed from the obtained LMIs. Furthermore, the developed results unify H∞ and passive filtering problems in a single framework. Finally, two numerical examples including an application-oriented example are provided to demonstrate the effectiveness of the proposed filter design technique.