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

M. Sathishkumar, R. Sakthivel, O. M. Kwon and B. Kaviarasan

International Journal of Systems Science, 2017, vol. 48, issue 7, 1416-1427

Abstract: 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.

Date: 2017
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DOI: 10.1080/00207721.2016.1261199

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