Control For Singular Markovian Jump System With Time-Varying Delays

Compared with the common Markovian jump systems,the singular Markovian jump systems can better describe the characteristics of the practical engineering systems,and time delays are also common in the practical engineering systems and ha ve a great impact on the performance of the systems.Based on this,the control problem of singular Markovian jump systems with time-varying delays is studied in this paper.The main research contents of this paper are as follows:1.The problem of H_∞ sliding mode control for a class of singular Markovian jump systems with time-varying delays is studied.Firstly,the integral sliding mode surface is designed to obtain the system model under the sliding mode.Secondly,by constructing a delay-dependent Lyapunov-Krasovskii functional,the sufficient conditions are given in the form of Linear matrix inequality(LMI)to satisfy the stochastic admissibility and H_∞ performance.Then,the controller is designed by methods like variable transformation to meet the requirements above,and then a sliding mode control law is designed to ensure that the sliding mode trajectory can reach the sliding mode surface in finite time.Finally,a numerical example is given to illustrate the effectiveness of the proposed method.2.The robust H_∞ sliding mode control problem for singular Markovian jump systems with parametric uncertainties and time-varying delay is studied.By constructing a delay-dependent Lyapunov-Krasovskii functional and combining inequality scaling lemmas,the sufficient conditions are given to satisfy the stochastic admissibility and H_∞ performance.,and a state feedback controller is designed by methods like variable transformation to meet the requirements above.Finally,the rationality of the designed controller is demonstrated by numerical simulation.