Stability analysis and stabilization for nonlinear continuous-time descriptor semi-Markov jump systems

This paper investigates the stochastic stability and the state feedback control design for a class of nonlinear continuous-time descriptor semi-Markov jump systems whose transition rates are time-varying, which are more general than the descriptor Markov jump systems. First, by deriving the infinitesimal generator for stochastic Lyapunov functional of descriptor semi-Markov jump systems, a stochastic stability condition is established, which guarantees this kind of systems are regular, impulse-free, have a unique solution, and are stochastically stable. In order to design the state feedback controller, a linear matrix inequality (LMI) stability condition is developed based on the lower and upper bounds of the time-varying transition probability and singular value decomposition approach. Furthermore, the state feedback controller design is developed in terms of LMI approach. Last, numerical examples are given to demonstrate the effectiveness of the obtained methods.