Research On Robust Stability And Control For Uncertain Systems

In most real engineering systems, it is almost impossible that the accurate mathematics model for the controlled plant is obtained since the uncertainty of the system is existent more or less. The uncertainty mathematics model may more factually describe the real control system and depict parameter perturbation and external disturbance of the system. Therefore, the research on robust stability and robust control for uncertain systems is significant in both theory and practice.This dissertation considers the problems of robust stability and robust control for uncertain systems. It is summarized that the model classification and suitable research methods of uncertain systems, robust stability and robust stabilization for interval systems, the guaranteed cost control of uncertain systems with time-delay, nonfragile guaranteed cost control for a class of uncertain nonlinear systems with time-delay, and the guaranteed cost control for nonlinear networked control system. The main contents and innovations in this paper are as follows:1. The model classification of uncertain systems is considered. We first describe the parameterized and non-parameterized uncertain modeles respectively, and sum up the modeling methods. Then the model classification method of uncertain systems is given and expressions are presented for different uncertain systems. And the research methods for different uncertain systems are analysed.2. The robust stability for interval systems is considered. We first study the robust stability for multiplicative interval systems. Some necessary and sufficient conditions of single-multiplicative interval systems are given, and a supposition necessary and sufficient condition of multi-multiplicative interval systems is presented. Then we consider the robust stability for interval systems. Some robust stability sufficient criteria are presented respectively. At last, we present a robust stability criterion of nonlinear interval systems.3. The robust stabilization for interval systems is considered. We first study the stabilizability for multiplicative interval linear systems. Some necessary and sufficient conditions of single-multiplicative interval systems are given, and some stabilizability sufficient criteria of multi-multiplicative and additive interval systems are presented. Then we consider the design problem of robust stabilization controller for interval linear and nonlinear systems. Some design algorithm of robust stabilization controller for interval systems are proposed.4. The guaranteed cost control problem for uncertain systems is considered. We first study the guaranteed cost control problem for uncertain time-delay nonlinear systems. Some existence sufficient conditions and design algorithm of guaranteed cost control law are given. For a class of uncertain nonlinear systems with time delay, with respect to perturbations in the controller coefficients, the nonfragile guaranteed cost control problem is considered, and the existence conditions and the design approach of nonfragile guaranteed cost control law are presented.5. The guaranteed cost control problem for networked control systems is considered. Firstly, the networked control system model with random time-delay is simplified and transformed into a discrete-time system model with uncertain parameters. Then the existence conditions and the design approach of guaranteed cost control law are presented based on the model educed.