Reduced-Order Filtering for Singular Markovian Jump Systems with Incomplete Transition Rates

This paper considers the reduced-order $H_{\infty }$ filtering problem for singular Markovian jump systems (SMJSs) with incomplete transition rates (ITRs) by using augmented system method. The considered conditions in this paper are necessary and sufficient (NS), whereas the existing conditions are mainly sufficient. To be concrete, by extracting system matrices in the considered system from augmented system, NS condition for the existence of the full-order $H_{\infty }$ filtering is provided in terms of linear matrix inequalities (LMIs). However, it is hard to extend the condition to the existence of the reduced-order $H_{\infty }$ filtering. Thus, by fixing augmented system matrices, NS condition for the existence of the reduced-order one is presented to guarantee the desired filtering error system to be stochastically admissible with $H_{\infty }$ performance level. Furthermore, there are neither complicated matrix transformation nor equality/rank constraints in this paper. One numerical and one practical examples are illustrated to demonstrate the effectiveness of the achieved results.