Synchronization Of Delayed Singular Lur'e Systems With Markovian Jumping Parameters

This paper is concerned about the synchronization problem of Lur'e system.Taking the advantage of that the singular Markov jump system can describe stochastic system,and considering the time-delay problem which is widely involved in the practical system,this paper studies the master-slave synchronization problem of delayed singular Lur'e system with Markovian jumping parameters.In addition,the robust synchronization problem is also studied when considering the uncertainty of system parameters.By constructing the synchronization error system and designing the controller by the state feedback control,the dynamic output feedback control and the sampled-data control respectively,the synchronization of the master-slave system is completed.The main work is as follows:1.The synchronization of delayed singular Lur'e ystem with Markovian jumping parameters is completed by using state feedback control method.The synchronization error system is constructed by analyzing the mathematical model of the master-slave system and state feedback controller,and then the synchronization problem is transformed to the stochastic admissibility problem.In order to obtain the stochastic admissibility criterion of delayed singular Lur'e system with Markoian jumping parameters,a mode-dependent and delay-dependent Lyapunov-Krasovskii functional is introduced and the conservation is analyzed by a numerical example.Based on the criterion,the design method of state feedback controller is obtained by linear matrix inequality(LMI)technology.Then,concerned about the parameter uncertainty,the design method of robust state feedback controller is obtained.2.The synchronization of delayed singular Lur'e system with Markovian jumping parameters is completed by using dynamic output feedback control method.The augmented synchronization error system is constructed by analyzing the mathematical model of the master-slave system and dynamic output feedback controller system.The design method of the controller to synchronize the master-slave system is obtained by LMI technology based on the stochastic admissibility criterion of delayed singular Lur'e system with Markoian jumping parameters.The robust dynamic output feedback controller design method is also considered.3.The synchronization of delayed singular Lur'e system with Markovian jumping parameters is completed by using sampled-data control method.The synchronization error system is constructed based on the master-slave system and sampled-data controller.A new piecewise Lyapunov-Krasovskii functional is introduced based on the above Lyapunov-Krasovskii functional.The design method of sampled-data controller to achieve the stochastic admissibility of the synchronization error system is obtained by LMI technology.All results in this paper are expressed by strict LMIs which could be solved by computer software.The effectiveness of the design methods is verified by some numerical examples at the end of each chapter.