Robust Stability And Robust Control For Uncertain Singular Systems

In this dissertation, a detailed analysis of the current situation of study on robust control of uncertain singular systems is given, and a study of the problems of robust stability and robust control for uncertain singular systems are stressed. The main results in this dissertation are as follows:1.The problems of stability for a class of linear time-varying singular systems and nonlinear singular systems are studied. A robust stability boundary of uncertain singular systems is proposed by utilizing singular value decomposition and the character of mode matrix.2.Robust stabilization for uncertain singular systems is investigated. Firstly, the robust stabilization of discrete singular systems with norm-bounded parameters uncertainty is explored. A good result is obtained through which we can find out the robustness of the considered systems only by computing a relevant matrix inequality for all the admissible uncertainty. Next, the robust static output feedback problems of uncertain singular systems with norm-bounded are studied. Necessary and sufficient conditions of static output feedback robust stabilization are given by using a class of generalized algebraic Riccati equations.3.Pole assignment for uncertain singular systems with D-stability is discussed. First of all, the concept of generalized quadratic D-stabilizability is put forward for uncertain singular continuous-time systems and uncertain singular discrete-time systems respectively. A method is proposed for designing the generalized quadratic D-stabilizer. Secondly, robust static observers are developed for uncertain singular systems with D-stability constrains. The singular robust static observer is presented just by using matrix inequality and generalized inverse theory. Sufficient condition for the existence of desired robust state observer is obtained and the analytical expression of the observer gain is derived.4.Robust H_∞ control is discussed for uncertain singular systems and...