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 discretetime switched systems with nonlinear perturbation are studied directly. First, with the iterative method, the analytical solution of the state equation for the asynchronously switched closedloop system is obtained. By analyzing the state solution of the closedloop system with the average dwell time method, sufficient conditions for exponential stability of closedloop 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 finitetime control problem is investigated for a class of continuoustime switched systems with nonlinear perturbation. Based on the analytical solution of the switched closedloop system, with the help of the GronwallBellman inequality and average dwell time method, sufficient conditions for finitetime stability of closedloop system are established. State feedback controllers are designed in terms of linear matrix inequalities. The algorithm to compute 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 modedependent average dwell time method, the asynchronous Hâˆž control problem is investigated for a class of switched timevarying delay systems. Time delays that appear in both the state and the output are considered. First, the concept of weighted Hâˆž performance is introduced into switched systems with modedependent average dwell time. By the utilization of the piecewise Lyapunov function approach, sufficient conditions that ensure the exponential stability and a weighted Hâˆž performance level for the closedloop system are proposed. Second, two types of smaller modedependent 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 Hâˆž dynamical output feedback controller that guarantees the exponential stability and a weighted Hâˆž performance level of the system is designed. The algorithm to compute the dynamical output feedback controller and the modedependent average dwell time is constructed. A numerical example is provided to illustrate the effectiveness of the proposed algorithm.
