Absolute Stability Analysis And Control Of Switched Lurie Systems

As a typical class of nonlinear systems,Lurie systems can be depicted by a junction of a linear dynamic system and a nonlinearity feedback,which are widely used in engineering field.In the actual system,due to the complexity of the system itself or external environmental factors,the system model with switching characteristics can better describe the complex dynamic process of the system.Therefore,the switched Lurie systems have important research value.Stability is an important property of system dynamics and a performance index that all automatic control systems must meet.The stability of Lurie systems is called absolute stability.At present,the research on the absolute stability of switched Lurie systems is still in the initial stage.Therefore,it is of great theoretical significance and practical value to establish an easily verifiable absolute stability criterion for the system based on the nonlinear constraints,and then design the feedback controller and switching signal to realize the absolute stabilization control of the system.Based on the above problems,this paper carries out systematic and in-depth research to enrich and improve the theoretical system of absolute stability of switched Lurie systems.The main contents include absolute stability analysis,absolute exponential stability analysis for time-varying delay,absolute stabilization analysis based on output feedback controller,H∞ control based on state feedback controller,and asynchronous control.Specifically summarized as follows:1.Based on dwell time switching technique,the absolute stability of switched Lurie systems is studied.By constructing a class of switched time-varying Lyapunov-Lurie functions and designing mode-dependent dwell time switching signals,the absolute stability criteria of switched Lurie systems are given.Furthermore,the conservatism of this method in absolute stability analysis is studied.Finally,simulation examples show the rationality of the proposed method.2.The absolute exponential stability of switched Lurie systems with time-varying delay is studied by using Lyapunov-Razumikhin function technique.By constructing a switching time-varying Lyapunov-Razumikhin function,the sufficient conditions are given to guarantee the absolute stability of switched Lurie systems under the mode-dependent dwell time switching signals.Finally,numerical examples verify the effectiveness of the theoretical results.3.The absolute exponential stability of switched time-delay Lurie systems with multiple nonlinear feedback controls is investigated.For switched Lurie systems with all subsystems unstable,absolute exponential stability conditions are obtained by designing the mode-dependent interval dwell time switching signal and constructing the switching timevarying Lyapunov-Razumikhin function.Moreover,the theoretical results are extended to the stability analysis of switched delay Hopfield neural network.4.The absolute stabilization of switched Lurie systems is studied.Based on switching time-varying Lyapunov-Lurie function and mode-dependent dwell time technique,a class of dynamic output feedback controllers with time-varying control gain is designed.The feasibility of the control is improved by employing the projection lemma instead of the usual variable substitution technique.On this basis,the criterion of absolute stability under modedependent dwell time switching is derived.The problem of solving dynamic output feedback controller is transformed into a convex optimization problem of linear matrix inequality.5.The problems of L2-gain and H∞ control for switched Lurie systems are studied.By constructing the switched time-varying Lyapunov-Lurie function,the L2-gain criterion of switched Lurie systems under mode-dependent dwell time switching is given.Based on the time-varying control strategy,a state feedback controller with time-varying control gain is designed,and the control synthesis conditions are established to make the closed-loop switched Lurie systems absolutely stable and have H∞ performance index.Finally,the effectiveness of the controller is verified by flexible joint robotic arm model.6.Considering the asynchronous problem of the underlying plant change and activation of its candidate controller,the absolute stability and H∞ control for switched Lurie systems with asynchronous switching are studied.Aiming at the characteristic of asynchronous switching,a controller-dependent switched time-varying Lyapunov-Lurie function is constructed.Based on the mode-dependent minimum dwell time switching method,the absolute stability criterion of switched Lurie systems under asynchronous switching is given.On this basis,based on the switched time-varying Lyapunov-Lurie function,time-varying control scheme is designed.By linear matrix inequality technique,H∞ control synthesis conditions are established.They are further verified by simulation examples.