Bumpless Transfer For Switched Linear Systems With Stability And Performace Guarantee

As a class of hybrid systems,the switched system consists of a family of subsystems and a switching signal that regulates the switching between them.The switched system has attracted much attention in the last decades because of its important theoretical significance and extensive practical background.However,most of the studies on switched systems focus on the steady-state performance rather than the transient behavior,especially the one caused by switchings.In fact,the switching among candidate controllers may cause large variations of the control signal,which may degrade the transient performance of the system and even destabilizes the closed-loop system.The discontinuity may also damage the actuator in many practical situations.In order to suppress the undesired transient behavior,bumpless transfer control is proposed.Aiming at the shortcomings of some existing bumpless transfer control methods and based on the idea of ideal transition curve approximation,design methods of bumpless transfer controllers with stability and H? performance guarantee for switched linear systems with persistent dwell time(PDT)switching are presented in this paper.With the presence of amplitude-bounded disturbances,the algorithm to compute a robust positive invariant(RPI)set is also given.The main result of this dissertation are summarized as follows:(1)Bumpless transfer for discrete-time switched linear system with stability guarantee.In this part,the ideal transition curve,the controller with a segmented structure and the bumpless transfer performance index is given first.The existence of the bumpless transfer controller is regarded as an asynchronous switching phenomenon and the global uniform asymptotic stability(GUAS)condition for closed-loop switched linear systems with asynchronous PDT switching is proposed.Then the linear matrix inequalities(LMIs)of the stability condition are given,which are used as constraints on the optimization problem to achieve the solving of the bumpless transfer controller with stability guarantee.(2)Bumpless transfer for discrete-time switched linear system with energy bounded disturbance.The stability and l2-gain analysis for switched linear systems with PDT switching and energy bounded disturbance are discussed.The GUAS condition with an l2-gain for closed-loop switched linear systems with asynchronous PDT switching is proposed.The LMIs of the stability condition with an l2-gain are given,which are used as constraints on the optimization problem to form a compete design method of bumpless transfer controller with H? performance guarantee.(3)Bumpless transfer for discrete-time switched linear system with amplitude bounded disturbance.First,the bumpless transfer controller with stability guarantee is designed for the nominal system corresponding the switched linear system with PDT switching and amplitude bounded disturbance.Then,the control law and the error system are given according to the tube-based control methodology.Finally,the algorithm to compute a mode-dependent PDT RPI is presented,which ensures that the error between states of the nominal and disturbed systems within the RPI.(4)Numerical simulations are carried out to verify the effectiveness of the designed bumpless transfer controllers and the validity of the proposed methodologies.