Robust Non-fragile H_∞Control For Singular Systems With Linear Fractional Parametric Uncertainties

Singular systems theory has been developed profoundly since its beginning. Recently the singular systems with uncertainty and time-delay have been paid special attention by the researchers because of comprehensive practical application background. However, most results are under the assumption that the designed controller can be exactly implemented. When the controller can’t be exactly implemented, we should design non-fragile controller for uncertain singular systems. The considered uncertainties are linear fractional. The main contents are as follows.(1) The background, the development of the theory and recent research achievements of singular systems with uncertainty and time-delay are introduced respectively. H∞robust control and non-fragile H∞control are also introduced respectively. The main results are presented. Some basic knowledge and lemmas, which will be used later, are presented in chapter two.(2) The problem of robust non-fragile H∞control is studied for a class of singular systems with time-delays exist both in the state and control input. Using Lyapunov theory and linear matrix inequality technology, the design method of the non-fragile state feedback controllers is given. Design of the state feedback non-fragile controller is given in terms of linear matrix inequalities. The obtained robust non-fragile H∞controller guarantees the asymptotic stability of the closed-loop system.(3) The problem of robust non-fragile H∞control and robust non-fragile H∞guaranteed cost control are studied for a class of singular systems with time-varying delays. The time delays are time-varying and exist both in the state and control input. The robust non-fragile H∞controller and non-fragile H∞guaranteed cost controller are designed. (4) The robust non-fragile H∞control problem is studied for a class of singular systems with multiply time-delay. Based on the linear matrix inequality technology, the sufficient condition for the existence of robust non-fragile controller is given, and the controller design method is also derived.The conclusions in this paper are mainly expressed as linear matrix inequalities, therefore MATLAB can be used to obtain the solutions conveniently. Then we give relative numerical examples to demonstrate the feasibility and effectiveness of the results obtained.