Finite-Time Stability Analysis And Design For Switched Systems

As an i mportant class of hybrid dyna mical system s, s witched system s are composed of several continuous-time subsystems or discrete-time subsystems and the switching signals am ong them . W ith their own particularity, they differ from the traditional continuous-time systems or discrete-time systems. Therefore, it is necssary to investigate the switched system s. Duri ng the last several decades, there is an increasing interest on the m odeling, analysis and control of switched systems. However, most of the e xisting results concentrate on the as ymptotic stability in the infinite-time interval.The main contents of this thesis are as follows:First, the finite-tim e stability analysis for a class of continuous-tim e switched systems with impulsive effect is studied. The switched systems are composed of both Hurwitz stable and unstable subsystems. Based on the average dwell time method and by dividing the total activation time into the time for stable subsystems and the time for unstable subsystems, it is shown that we do not need the activation time for stable subsystems is larger than the activation time for unstable subsystems if we require the given switched system finite-time stable with a desired stability margin.Second, the problem of finite-tim e stab ility analysis is considered for discrete-time impulsive switched systems. The switched system is composed of Schur stable and unstable subsystem s. Sim ilar to the continuous-tim e case, we derive a criterion under which the finite-time stability can be realized.Third, the design problem of state f eedback controller for finite-time stability is studied. A sufficient condition is proposed to ensure finite-tim e stability of linear switched systems. Based on it, the state feedback controller design m ethod is given to satisfy the input constraints.