Optimal H-infinity filtering for singular Markovian jump systems

Abstract

This paper considers H-infinity filtering for continuous-time singular Markovian jump systems (SMJSs). While the existing researches in the literature suggested only sufficient conditions in terms of strict or non-strict linear matrix inequalities (LMIs) for sub-optimal H-infinity filtering, this paper successfully derives a necessary and sufficient condition in terms of strict LMIs for optimal H-infinity filtering. First, the necessary and sufficient condition that guarantees the stochastic admissibility of the filtering error system is obtained in terms of matrix inequalities. To reformulate it into strict LMIs, the congruence transformation by specially designed matrices is used. Two numerical examples show the validity of proposed H-infinity filtering. (C) 2018 Elsevier B.V. All rights reserved.