On Finite-time Boundedness For Switched Time-Delay Systems

Switched system is a kind of important models to study hybrid systems from the perspective of system and control science. From the system theory point of view, the states of any practical systems depend on the past states. Therefore, time-delay is a common phenomenon in real-world engineering systems. Switching and time-delay often lead to instability and poor performance, and greatly increase the difficulty of stability analysis. In addition, finite-time boundedness focuses on the dynamic behavior of the system in a finite time interval, which has some engineering application background and is different from the Lyapunov asymptotical stability. Thus, the investigation of finitetime boundedness for switched time-delay systems is of great theoretical and practical significance.This thesis concerns with the finite-time boundedness of switched time-delay systems. The main contents are listed as follows:First, the problem of finite-time boundedness for switched linear systems subject to discrete time-varying delays is considered. By combining the Jensen inequality and multiple Lyapunov functionals, time-dependent approach is utilized to investigate the finite-time boundedness of switched time-delay systems. The corresponding switching signals are also designed and a sufficient condition is derived to guarantee the finitetime boundedness of the switched systems. It is shown that the obtained result can achieve less conservativeness comparing with the previous ones.Second, we focuse on switched systems subject to both discrete and distributed delays. Based on the average dwell time, we derive the finite-time boundedness conditions for switched distributed delay systems according to the Jensen inequality and the Wirtinger inequality, respectively. Then, the simulation example is provided to illustrate the validity of our results.Finally, the problem of finite-time boundedness for switched neutral systems is discussed. By combining the Wirtinger inequality and the reciprocally convex approach, we propose the mode-dependent average dwell time technology to design switching signals to guarantee the finite-time boundedness of the switched systems.