Robust control for Markovian jump systems with partially known transition probabilities and nonlinearities

This paper investigates robust H∞ controller design for Markovian jump systems (MJSs) with partially known transition probabilities (TPs) and nonlinearities. A general nonlinearity model is proposed, the generalization lies in three aspects: (1) the nonlinearities include both state and delayed state information; (2) the nonlinearities satisfy sector-bounded conditions; (3) apart from the lower and upper bounds, the probability information of the nonlinearities belonging to different sector bounds is utilized. The MJSs are considered with some of the TPs completely unknown, which can cover the MJSs with completely known TPs and completely unknown TPs as special cases. It should be noted that the relationship between known and unknown TPs is utilized, which can reduce the conservatism of the results. By using the Lyapunov functional method, sufficient conditions are derived. At last, two simulation examples show the application and effectiveness of the proposed method.