H∞H∞ and H2H2 filtering for linear systems with uncertain Markov transitions

This paper is concerned with H∞H∞ and H2H2 filtering for Markovian jump linear systems with uncertain transition probabilities. Motivated by the fact that the existing results either impose severe restrictions on some key matrices or introduce some unnecessary matrix variables, this paper is focused on developing a new approach to systematically relax these restrictions for filter design. By applying a novel technique to eliminate the product terms between the Lyapunov matrices and the filter parameters, an improved condition is first obtained for analyzing the H∞H∞ performance of the filtering error system. Then sufficient conditions in terms of linear matrix inequalities are presented for designing filters with a guaranteed H∞H∞ filtering performance level. The proposed method is further extended to H2H2 filtering. Theoretical analyses followed by a few numerical examples show that the proposed filter design method outperforms some existing results with respect to reduction of conservatism or variables needed for computation. The filter design problems for both continuous-time and discrete-time Markovian jump linear systems are addressed in a unified framework.