Stability Analysis And Control Of Delay Systems Based On Switching Technique

Time delays are often encountered in many real control systems,such as networked control systems,power systems,etc.Since time delays may cause poor performance and even lead to instability,considerable attention has been paid to time delay systems.The Lyapunov-Krasovskii functional(LKF)approach is an efficient tool to deal with the problem of stability analysis and control for time delay systems.Although a large number of improved methods have emerged in the framework of the LKF method,the delay variation information is not adequately considered.Thus,there still exist some room for improvement.With the help of the switching method,this thesis,based on previous work of others,fully uses the delay variation information and deeply investigates the problem of stability and control for time delay systems.The main contents of this thesis are given as follows:Based on the limitations of the existing stability analysis methods for delay systems,the idea that the delay variation information should be adequately considered is proposed.The time-delay interval is divided into some smaller variable intervals.Based on the switching idea,the smaller variable interval can be viewed as a mode of the delay and the delay variation can be viewed as the switching among the modes.Then,delay systems can be modeled as switched delay systems containing stable subsystems.The new model is equivalent to the original system and contains more usable delay information.Based on the new model,the mode-dependent average dwell time(MDADT)method,which is more effective than the LKF method,is adopted to obtain stability criteria for linear continuous/discrete-time systems.The relationship between the conservativeness of the obtained results and the number of subsystems is also investigated.Based on the MDADT method,a new switching method is proposed to deal with the prob-lem of stability analysis and stabilization for neutral delay systems.Neutral delay systems are modeled as switched neutral delay systems and then exponential stability criteria are obtained by adopting the MDADT method.Based on the obtained stability conditions,a new switching method,which can relax the constrained switching conditions in the MDADT method,is pro-posed and new exponential stability criteria are derived by using the method.With the help of the obtained criteria,the switching controller is used to solve the stabilization problem of neutral delay systems and new stabilization conditions are obtained.The proposed stabilization strategy is significantly less conservative due to the full use of time delay variation information and its avoidance of using a common controller for the entire delay interval.The problem of L2 gain analysis and control for delay systems is solved by using a slow switching method.The L2-gain analysis problem of delay systems is converted into the L2-gain analysis problem of switched delay systems.Based on a slow switching strategy,new L2-gain conditions are obtained and then the conditions for the existence of the L2-gain controller are given.The problem of guaranteed cost control for uncertain systems with large delay periods(LDPs)is studied.The considered systems are modeled as switched delay systems containing a stable subsystem and an unstable subsystem.Then,sufficient conditions under which the guaran-teed cost controller can keep the systems stable and guarantee an adequate level of performance are obtained by adopting a slow switching method.The effect of time delays on the stability of nonlinear system is considered and the stability analysis problem of delayed neural network systems is solved.Delayed neural network systems are modeled as nonlinear switched delay systems.The stability analysis problem of delayed neu-ral network systems is converted into the stability analysis problem of switched systems.Then,switching methods are used and new stability conditions are derived to ensure the exponential stability of delayed neural networks.Since controller failures may occur in actual systems,the stability analysis problem of multi-area power systems with time delay under controller failures is considered.In order to describe the phenomenon that the controller is completely invalid and can restore normal work after a period of time,the considered systems are modeled as switched multi-delay systems containing a stable subsystem and an unstable subsystem.Based on the new model,sufficient stability conditions which can guarantee the stability of the considered systems are obtained by using a slow switching method.