Asynchronous Control Of Several Classes Of Switched Systems

As an important class of hybrid systems, switched systems consist of a finite number of subsystems and a switching signal orchestrating the switching among them, with a wide range of their applications in nature, engineering, and social sciences. In recent years, switched systems have been researched deeply, and many results have been obtained. For the control problem of switched systems, it is generally assumed that the subsystems and the controllers run synchronously. However, in actual operation, it takes some time to identify the active subsystem and apply the matched controller, so the switching of the controllers experiences a time delay with respect to that of subsystems, which results in asynchronous switching. In this dissertation, the asynchronous control problems of several classes of switched systems are investigated. The main works are as follows:By analyzing the state solution of the system, the dynamics of the discrete-time switched systems with nonlinear perturbation are studied directly. First, with the itera-tive method, the analytical solution of the state equation for the asynchronously switched closed-loop system is obtained. By analyzing the state solution of the closed-loop sys-tem with the average dwell time method, sufficient conditions for exponential stability of closed-loop system are established. Then, Based on the obtained sufficient conditions, the state feedback controllers are designed in terms of linear matrix inequalities. At last, the algorithm to compute the state feedback controller and the minimal average dwell time is constructed. Without using any Lyapunov function, the solution analysis method provides a new research idea for the switched systems.By the use of the average dwell time method, the asynchronous finite-time control problem is investigated for a class of continuous-time switched systems with nonlinear perturbation. Based on the analytical solution of the switched closed-loop system, with the help of the Gronwall-Bellman inequality and average dwell time method, sufficient conditions for finite-time stability of closed-loop system are established. State feedback controllers are designed in terms of linear matrix inequalities. The algorithm to com-pute the state feedback controller and the average dwell time is constructed. At last, a numerical example is given to demonstrate the effectiveness of the proposed method.Based on the mode-dependent average dwell time method, the asynchronous H∞ control problem is investigated for a class of switched time-varying delay systems. Time delays that appear in both the state and the output are considered. First, the concept of weighted H∞ performance is introduced into switched systems with mode-dependent average dwell time. By the utilization of the piecewise Lyapunov function approach, suffi-cient conditions that ensure the exponential stability and a weighted H∞ performance level for the closed-loop system are proposed. Second, two types of smaller mode-dependent average dwell time are designed by dividing all the subsystems into two parts based on the values of the selected parameters. At last, the asynchronous H∞ dynamical output feed-back controller that guarantees the exponential stability and a weighted H∞ performance level of the system is designed. The algorithm to compute the dynamical output feed-back controller and the mode-dependent average dwell time is constructed. A numerical example is provided to illustrate the effectiveness of the proposed algorithm.