Exponentially Dissipative Control Of Singular Markovian Jump Systems With Time Delay

Markovial jump system is a kind of special hybrid system,which can better describe the random mutation of the physical system,and it has been widely used in communica-tion systems and control systems,such as statellite systems and chemical industry process control and so on.It is in order to solve the actual needs,so more and more scholars and engineers pay more attention to the research of the singular Markovian jump systems with time-delay.In this paper,we study the exponentially dissipative control of singular Markovian jump systems with time delay.The main contents are as follows:1.The exponentially dissipative control and exponentially passive control of singular Markovian jump systems with mixed mode-dependent delays axe investigated.Firstly,we obtain the sufficient condition by applying a novel Lyapunov function including mode-dependent double integral terms.Then,we design the dissipative state feedback controller.Finally,we study the dissipative problem of the system with uncertain parameters.2.The exponentially dissipative control and exponentially passive control of dis-persed singular Markovian jump systems with mixed mode-dependent delays are studied.Firstly,the sufficient condition is obtained by using Lyapunov functional method and LMI approach.Then the dissipative state feedback controller is designed,which guarantees the closed-loop system to be exponentially dissipative.Finally,the dissipative control problem of the systems with uncertain parameters is studied.3.The exponentially dissipative control and exponentially passive control of singular Markovian jump systems with mode-dependent time-varying delays and forgetting time delay are studied.The sufficient condition is obtained by combining the free-weighting matrix and week infinitesimal operator approach.