Study Of Event-Triggered Control Of Switched Linear Systems

Switched systems belong to an important class of hybrid systems, and the hybrid characteristic of switched systems lies in that there exist interacting continuous dynamic signals of the subsystems (or modes) which are described by differential equations or difference equations and a switching signal that orchestrates the switching among these subsystems and takes values in a finite positive integer set. As the switching character-istic exists in a variety of physical plants, hence switched systems have a broad range of practical application areas. Moreover, in the theoretical research line of switched systems, the stability and stabilization problems of switched systems have been the hot topics in the field of control and systems for a long time, on which quite a lot of re-search results have appeared. On the other hand, with the extremely rapid development of the network level of modern control systems, the contradiction between the limited communication resource and the increasing control tasks has become much more obvi-ous. Therefore, in order to overcome the drawbacks arisen from the conventional time-triggered mechanism, compared to which, a new triggering mechanism, i.e., the event-triggered mechanism is proposed. Extensive attention has been paid to event-triggered mechanism, as it can significantly reduce the communication frequency between the controllers and the sensors while guaranteeing a satisfactory system performance. To date, the event-triggered mechanism has been applied to lots of systems, and quite a few valuable results have been achieved. However, it should be pointed out that the prob-lem of event-triggered control for switched systems has not been well addressed yet. Thus, this dissertation introduces the event-triggered mechanism to switched system-s and investigates the event-triggered controller design problem for switched systems. The main work of this dissertation can be concluded as follows:Firstly, for switched systems without time delays and exogenous disturbance input-s, we design the event mechanism (event-triggers), the event-triggered state feedback controller, and the event-triggered output feedback controller when the system states are available for feedback and unavailable for feedback, respectively. Then, via the average dwell time (ADT) method and Lyapunov function technique, some sufficient conditions that can ensure the event-triggered switched system finite-time stabilization are given in the form of linear matrix inequalities (LMIs). A numerical example is carried out to illustrate the effectiveness of the obtained theoretical results.Secondly, the problem of event-triggered control for switched systems with time-varying delays is researched. With the above-mentioned state-based and output-based (or observer-based) event-triggers, the event-triggered state feedback controller and the event-triggered output feedback controller are designed for switched delay systems, respectively. Then, via the ADT method and Lyapunov-like function technique, some sufficient conditions that can ensure the event-triggered switched delay system finite-time stabilization are given in the form of LMls. A numerical example is performed to show the validness of the proposed design methods.Finally, the event-triggered H∞ control problem is considered for switched delay systems with exogenous disturbance inputs. The event-triggered state feedback H∞ controller and the event-triggered output feedback H∞ controller are synthesized when the system states can be measured or not, respectively. Additionally, some sufficient conditions of LMls form are presented to guarantee the system H∞, stabilization via the ADT method and Lyapunov-like function technique. Simulation results demonstrate the potential of the obtained control and design approaches.This dissertation proves the feasibility of the application of event-triggered mech-anism to switched systems by means of theoretical derivation. Besides, the design approaches of the event-triggered state feedback controller, the event-triggered output feedback controller, and event-triggered H∞ controller are given and verified through simulation experiments.