Analysis And Synthesis Of Switched Systems With Actuator Saturation;analysis And Synthesis Of Switched Systems With Actuator Saturation

Switched systems are a class of hybrid dynamic systems which consist of a family of subsystems and a switching signal that orchestrates the switching among them. Since many practical engineering systems, such as aerospace, automotive industries, chemical process, transportation transmission, computer control systems, communications industries etc., can be modeled as switched systems, switched systems theory and switching control strategy have received domestic and foreign researchers'extensive attention in the past few years. On the other hand, for practical engineering systems, the restraints added by human and the inherent physical constraints from systems themselves exist in all actuators. Actuator saturation constraint is a common phenomenon, and saturation widely appears in the real control systems. However, as studies of switched systems theory concentrate on the subsystems which have simple and deterministic characteristics, and a lot of research focused more on continuous-time switched systems, the applications of switched systems theory in many practical areas have been limited in a great extent. This thesis, based on the previous works of others, systematically studies the analytical and synthetical problems of the polytopic uncertain discrete-time switched systems with input saturation constraint when they are in the average dwell-time switching ways. The study can be operated from the points including stability analysis, state feedback controller design, static output feedback controller design which are based on parameter-dependent switched Lyapunov function. In addition, an important class of switched systems, say, piecewise affine systems with saturation constraints are considered to use the static output feedback strategy.Firstly, we introduce the research background, the basic concept of switched systems, analytical methods, and the analytical methods of the saturation term, etc., which provide adequate theoretical basis for the following works. In this foundation, we aim to analyze the closed-loop stability and estimate the domain of attraction for a class of switched systems with average dwell-time and subject to input saturation based on three different Lyapunov functions, which are switched Lyapunov functions, parameter-dependent switched Lyapunov function and saturation-dependent switched Lyapunov function. We can offer three different analytical methods under average dwell time switching signal, and compare them to estimate the domain of attraction. Secondly, we can investigate the problem of state feedback control for polytopic type uncertain discrete-time linear switched systems with input saturation constraint. First of all, for the disturbance free case, we proposed a switched state-feedback controller guaranteeing the locally exponential stability of the resulting closed-loop system under average dwell-time switching scheme and estimate the domain of attraction based on parameter-dependent Lyapunov function. On this basis, considering the case of existence of disturbance in subsystems, we propose the anti-saturated H-infinity state-feedback controller for the saturated switched systems under average dwell-time switching scheme, the desired conditions for the existence of the controller can be solved by the corresponding linear matrix inequalities via convex optimization process.Then, we aim to design the static output-feedback controller for the polytopic type uncertain discrete-time linear switched systems with input saturation constraint under average dwell-time switching scheme and estimate the domain of attraction based on a parameter-dependent switched Lyapunov function method. Based on a matrix equations approach, bilinear matrix inequalities can be transformed into linear matrix inequalities. For the case of existence of disturbance in subsystems, we provide the anti-saturated and anti-disturbance H-infinity static output-feedback controller for the saturated switched systems under average dwell-time switching scheme. By introducing some slack variables bilinear matrix inequalities based on conditions, corresponding results can be obtained for the H-infinity static output-feedback controller design.Finally, two novel approaches of piecewise affine model based on static output feedback control have been developed for a class of constrained nonlinear processes. The congruence transformation, some bounding inequalities, and degenerate ellipsoid based on S-procedure techniques are used to recover the design convexity. The stability as well as the H-infinity control performance of the closed-loop system can be guaranteed by several sufficient conditions, which are cast into a number of linear matrix inequalities and by using piecewise quadratic Lyapunov functions, the conservatism of controller designs can be alleviated. Simulation examples are provided to demonstrate the effectiveness of the proposed approaches.