Stability and Stabilization for Singular Switching Semi-Markovian Jump Systems with Generally Uncertain Transition Rates

This paper studies the problems of stability and stabilization for a class of singular switching semi-Markovian jump systems. The general transition rates in the semi-Markov process cover completely unknown and uncertain bounded as two special cases. First, sufficient conditions are developed to ensure the unforced system to be regular, impulse-free, and exponentially mean-square stable. Then, by proposing a state feedback controller, sufficient conditions in terms of strict linear matrix inequalities are derived to guarantee the closed-loop system to be stochastically stabilziable. Finally, a numerical example is provided to show the effectiveness of the obtained results.