Research On Stability And Stabilization Of General Switched Systems

As a kind of important modeling tool,switched systems have been widely applied in networked control systems,servomechanism systems,robotic control systems,and elec-trical devices/circuits systems.Furthermore,the idea of switching is also common in the field of automatic control,such as the multi-mode controller and variate structure con-troller.Therefore,the research of the switched system has far-reaching engineering and academic significance.Switched systems consisted of stable subsystems are broadly ex-istent in our daily life,which has been discussed widely.However,controller failure or sensors fault is inevitable in the real world,which will make the stable subsystem unsta-ble.Therefore,the significance of switched systems with unstable subsystem also cannot be underestimated.So far,the related research results of this kind of switched systems are not very sufficient,and most of them could be further improved.Furthermore,for switched systems with a different combination of stable subsystems and unstable subsys-tems,the existing conclusions need to choose the corresponding analytical method.In this dissertation,the stability and stabilization problem of the general switched systems have been discussed,where the system can be composed of an arbitrary combination of stable and unstable subsystems.A unified analytical method was proposed,which reduces the conservatism of existing conclusions.The main results are summarized as follows:?1?Consider switched systems with all subsystems unstable,the stability problem under interval dwell time switching sequence has been discussed.In this dissertation,the state-transition matrix based method and the interpolation method have been adopted in stability analyses.And we have compared the difference between these two methods from Lyapunov function,conservatism,computation,and extendibility.In addition,with the state-transition matrix based method,we also have given the stability condition under floating interval dwell time switching signal.?2?Consider switched systems with all subsystems unstable,the stability condition under the average dwell time switching signal was proposed.Switchings can be classified into two categories depending on their dwell time,which are the stable switching without divergence time and the unstable switching with divergence time.Then,we defined the bounded maximum average dwell time,which describes the ratio between the divergence time and the number of switchings.We derived new stability condition with the bounded maximum average dwell time,where the state divergence caused by unstable switching could be compensated by stable switching.Compared with the stability condition under the maximum average dwell time,the new stability condition has lower conservatism,and the limitation about the minimum dwell time is not necessary.?3?Stability problem of general switched systems under mode-dependent average dwell time switching signal was discussed in the dissertation.Combined with subsystem characteristic and mode-dependent average dwell time technology,we classified the sub-systems into two categories:switching stable subsystems and switching unstable subsys-tems.Based on that,we proposed a new stability condition with mode-dependent average dwell time,which restraints the ratio of runtime between switching stable subsystems and switching unstable subsystem.Switching stability of subsystems have no direct relation-ship with their stability,any subsystem could be switching stable or not.Therefore,with a unified frame,we can analyze the stability problem of the general switched system which could be composed with stable subsystems,stable subsystems and unstable subsystem,or unstable subsystems.In addition,the fast switching strategy is available to unstable sub-systems,therefore unstable subsystems could switch to each other and the corresponding stability condition is more applicable to switched systems with more unstable subsystems.?4?Some subsystems may not be fully controllable,therefore the corresponding closed loop subsystem may be unstable.Based on the unified mode-dependent average dwell time stability condition,we designed a state feedback controller for the general switched system whose subsystems maybe uncontrollable.Meanwhile,we also discussed the dis-turbance attenuation properties of the general switched system under mode-dependent av-erage dwell time switching signal.Finally,the issues of L₂-gain analysis and H_?controller design for the general switched system are addressed.In this dissertation,we considered the unstable subsystems from a new perspective.A unified analytical method was proposed for general switched systems which improves the flexibility of the traditional one.In this dissertation,the main stability conditions are de-scribed with linear matrix inequalities?LMIs?,which can be solved easily with MATLAB LMI toolbox.Then,some numerical examples are given to demonstrate the feasibility and effectiveness of the results.