Mode-dependent robust and non-fragile finite-time H∞ control for nonlinear singular Markovian jump systems

This paper is concerned with the problem of mode-dependent robust and non-fragile finite-time H-infinity control for a class of nonlinear singular Markovian jump systems (NSMJSs) with parameter uncertainties and time-varying norm-bounded disturbance. Some sufficient conditions ensuring the singular stochastic H-infinity finite-time boundedness (SS H-infinity FTB) are developed for the given system by using the stochastic analysis and linear matrix inequality techniques. Then, a finite-time H-infinity state feedback controller is designed, which can guarantee the H-infinity finite-time boundedness of the closed-loop systems. Furthermore, a robust and non-fragile finite-time H-infinity state feedback controller is also provided to ensure the H-infinity finite-time boundedness of the closed-loop systems when the controller gain has an additive perturbation. Finally, two numerical examples are given to illustrate the effectiveness of the obtained results.