$$ H_{\infty } $$ H ∞ Filtering for Discrete-Time Singular Markovian Jump Systems with Generally Uncertain Transition Rates

This paper is devoted to the problem of $$ H_{\infty } $$ filtering for a class of discrete-time singular Markovian jump systems with generally uncertain transition rates. Each transition rate of the jumping process is completely unknown or only the estimated value is known. The objective is to design a $$ H_{\infty } $$ filter such that the resulting filtering error system is stochastically admissible (regular, causal and stochastically stable) while satisfying a prescribed $$ H_{\infty } $$ performance $$ \gamma $$ . Sufficient conditions are derived that can guarantee the filtering error system is $$ H_{\infty } $$ stochastically admissible. Moreover, explicit expression of the filter gains is obtained by solving a set of strict linear matrix inequalities. Finally, a numerical example is included to illustrate the effectiveness of the proposed method.