Robust Control Of Uncertain Switched Linear Discrete Time Systems With Time Delays

As a special class of hybrid systems, the switched systems are composed of a family of subsystems and a rule orchestrating the switching between the subsystems. With the development of science and technology, the problems encountered in many fields should be resolved by switched system theory.The Analysis and control of the switched systems become very difficult when time delays and uncertainties exist in real systems. Hence the study on robust control of uncertain switched systems with time delays is of great significance.This dissertation investigates the robust control of the switched linear discrete time systems with time delays. The main contributions of this dissertation are as follows.(1) The guaranteed cost control problem of the uncertain switched discrete time systems with delayed states and inputs is discussed for the quadrautic performance index. Based on the piecewise quadratic Lyapunov functions, the synthesis method of the guaranteed cost controllers with state-based switching law is developed. By the obtained control law, the perturbed switched discrete time systems can be asymptotically stabilized and the close loop cost is not greater than a specified upper limit for all admissible uncertainties.(2) By considering the controller perturbation, the non-fragile guaranteed cost control problem of the uncertain switched discrete time systems with multi-delays in states and inputs is discussed for the quadratic cost functions. Based on the piecewise quadratic Lyapunov functions, the synthesis method of the delay-dependent non-fragile guaranteed cost controllers with state-based switch law is proposed. Then a cone complementarity linearization algorithm is used to solve the non-linear matrix inequalities. By the obtained control law, the perturbed switched discrete time systems can be asymptotically stabilized and the close loop cost is not greater than a specified upper limit for all admissible uncertainties.(3) Due to the existence of the controller parameter uncertainties, the non-fragile robust H_∞. control problem is investigated for the polytopically uncertain switched discrete time systems with multiple state and input delays. The synthesis approach of the delay-dependent non-fragile H_∞controllers with state-based switch law is presented. The non-linear matrix inequality involved in the controller design is transformed into nonlinear programming problem constrained by non-linear matrix using a cone complementarity linearization algorithm.