Non-fragile H_∞ Control For Linear Discrete Singular Systems

Research of singular systems is introduced and then robust and time-delay theories of which are given. The significance of research is indicated and research background is given briefly. Based on theories of non-fragile H∞robust control and bounded real lemma, problems of non-fragile H∞control and non-fragile H∞robust control are discussed via matrix inequalities for cases of discrete singular systems and uncertain discrete singular systems and uncertain discrete singular systems with time-delay.(1) Non-fragile H∞state feedback control for discrete singular systems is investigated in chapter 2, a necessary and sufficient condition for existence of controller is obtained via bounded real lemma and LMI. Furthermore, the desired controller is presented via LMI. A simulation is given to illustrate effectiveness.(2) Uncertain discrete singular systems are studied in chapter 3. A neces-sary and sufficient condition of non-fragile H∞robust state feedback control is obtained via a similar method and the controller is provided via LMI. Then a simulation is also given to show the validity.(3) Non-fragile H∞robust state feedback control for uncertainty discrete singular systems with time-delays is discussed in chapter 4. The existence of H∞controller is analyzed and the desired controller is derived via bounded real lemma and LMI. A second method is given based on the system augmentation and matrix decomposition. Two simulations are given to illustrate the effectiveness.One innovation is that the necessary and sufficient condition can be obtained for the existence of non-fragile H∞controller or non-fragile H∞robust controller for systems without time-delays. And H∞controllers can be presented via LMI with less conservative. Another innovation is that existence of controller for time-delay systems can be derived via two methods, the corresponding controllers can also be presented via LMI with less conservative.