H_∞Control Of Switched Linear Parameter Varying Systems And Its Applications To Air Vehicles

A switched Linear Parameter Varying (LPV) system is a switched system whose subsystems are all LPV systems. Switched LPV systems have broad applications in en-gineering practice. Inherited both characteristics of LPV systems and switched systems, switched LPV systems can better describe practical systems and nonlinear systems. This makes it possible to apply linear system theory and control methods to practical systems and nonlinear systems. The study about the switched LPV systems is still limited and very few results have appeared. This dissertation studies the stabilization and the H∞problems of several kinds of switched LPV systems. The main contributions are as follows.Chapter2analyzes stability of a class of switched LPV systems in which state-space matrices are parametrically affine. For such a switched LPV system any subsystem is not assumed to be stable for parameters varying in a convex set. A switching law is de-signed to stabilize the switched LPV system through two methods in the chapter. By using the single Lyapunov function method, a sufficient condition for the existence of a parameter-dependent Lyapunov function and searching algorithms for feasible solu-tions are proposed. An Linear Matrix Inequality (LMI) condition for the existence of parameter-dependent Lyapunov functions is presented based on the multiple Lyapunov functions method. Two examples show the effectiveness of the proposed methods.Chapter3investigates stability and H∞performance problems for a class of discrete switched LPV systems in which all subsystems’state-space matrices are parametrically affine. Again, no subsystem is assumed to be stable for parameters varying in a con-vex set. A switching law is designed to stabilize the system with the H^, performance satisfied. By using the multiple Lyapunov functions method, LMI conditions for the ex-istence of parameter-dependent Lyapunov functions are proposed. An example shows the effectiveness of the proposed method.Chapter4studies the design problem of parameter dependent H∞filters for a class of switched LPV systems whose parameters are measurable. Conditions for existence of parameter-dependent Lyapunov function are proposed via parametrical LMI constraints. Based on the solutions to the LMIs, an algorithm for the gain matrices of LPV filter is presented. The design method is applied to a missile system to demonstrate the effective-ness.Chapter5is concerned with the switching control for an LPV polytopic system using multiple Lyapunov functions to improve the system’s H∞performance. For the large range of parameter varying, we divide the parameter region into small subregions and find a suitable Lyapunov function for each parameter subregion. Under the average dwell time switching logic, a sufficient LMI condition is proposed to guarantee the performance. The proposed control scheme is applied to an active magnetic bearing system.Chapter6presents a controller design method for dealing with the H∞performance problem of switched LPV systems. Considering the arbitrary switchings caused by the parameters varying, a common parameter-dependent Lyapunov function is employed to derive sufficient LMI conditions for the switched LPV systems. A family of LPV con-trollers are designed according to the LMI conditions, and each of them is suitable for the corresponding parameter region. The proposed switching LPV control method is applied to an F-16aircraft longitudinal model and simulation results demonstrate the effectiveness of the approach.Chapter7studies the H∞performance problem for switched LPV systems using a blending method. For a switched LPV system in which the parameters are grouped into slowly-varying and fast-varying parameters, the blending method and common Lya-punov function method are used to construct a blended Lyapunov function. The proposed method is applied to an F-16aircraft longitudinal model and the simulation results demon-strate the effectiveness of the approach.The conclusions and perspectives are presented in the end of the dissertation.