Robust H_∞ Control of Uncertain Nonlinear Continuous-Time Singular Semi-Markov Jump Systems

摘要

The robust state feedback H_∞ control problem for a class of uncertain nonlinear continuous-time singular semi-Markov jump systems is discussed in this paper. First, based on stochastic Lyapunov functional, a sufficient condition is established, which guarantees the uncertain nonlinear continuous-time singular semi-Markov jump systems are stochastically admissible and satisfy H_∞ performance. With this condition, based on the bounds of the time-varying transition probability, an LMI sufficient condition is given such that the singular semi-Markov jump systems are stochastically admissible and satisfy H_∞ performance. Then, the state feedback H_∞ controller design is developed in the LMI frame. Last, one numerical example is given to demonstrate the effectiveness of the obtained method.