Study Of Finite-time Stability And Control Of Switched Linear Systems

With the development of society, automatic control theory also encounters a varietyof challenges. The satisfactory control efect can not be obtained if the method whichsimply relies on continuous-time or discrete-time system is adopted. Therefore, hybridsystems has absorbed much attention. So far, the results focus on Lyapunov asymptoticalstability, which is a property defined in infinite time interval. In practical application,however, we usually pay attention to the dynamic behavior of the system in a finite timeinterval, i.e., finite-time stability property. Thus, the investigation of finite-time controlproblem of hybrid systems has far-reaching significance. This dissertation surveys therecent results on hybrid systems and gives a in-depth study on the finite-time controltheory.The main results in the frontier of switched systems and finite-time control are sum-marized and analyzed, and point out that the research on finite-time control problem ofswitched system is still in its infancy. Time-dependent approach is utilized to investigatethe Finite-Time Stability (FTS) and Finite-Time Boundedness (FTB) of switched systems.At the same time, the corresponding switching signals are designed, which can guaranteethat the switched system is FTB or FTS. The largest reginal function strategy is adoptedto define the switching signal, i.e., state-dependent method, and investigate the finite-timestability. The FTB and FTS can also be satisfied even if there exists the sliding motion.Based on this, time-dependent and state-dependent methods are utilized to designthe finite-time stabilizing controller and H∞controller for continuous-and discrete-timeswitched delay systems, respectively. When some state of switched systems are unmea-sured or there are not actual physical quantities that correspond to the states, observer-based mode-dependent state-feedback stabilizing and H∞controllers are designed to guar-antee that the corresponding closed-loop system is finite-time bounded.The asynchronous mode-dependent state-feedback controllers are designed, wherethe so-called asynchronous switching means that the switchings between candidate con-trollers and switched system modes are asynchronous. By combining merging switchingsignal technique and Average Dwell Time (ADT), finite-time stability problem is inves-tigated and corresponding mode-dependent state-feedback controller is designed. Next,time-dependent method is proposed to study the asynchronous finite-time stabilization of switched systems. It might seem that the dynamic state-feedback controller allowsus to meet more specifications than can be met using a static state-feedback. Thus, thefinite-time mode-dependent dynamic state-feedback stabilizing and H∞controllers aredesigned for continuous-time switched systems, which can guarantee the correspondingclosed-loop system is finite-time bounded and has a prescribed finite-time H∞perfor-mance.