Control For Linear Parameter-Varying Systems With State Delays

In physical systems,there exist various nonlinear and time-varying characteristics in different degree.And much attention has been paid to the study of linear parameter-varying (LPV) system because it can deal with the nonlinear and time-varying problems and its theory has been applied successfully in many fields such as aircraft,robot manipulators,and chemical process control.On the other hand,time delays,which are common in the number of industrial processes,will be a main source of bad performance or even instability for control systems.Therefore,it is noticed that the control problem of LPV systems with time delays has drawn increasing attention.The thesis,based on previous works of others, systematically and deeply investigates the problems of delay-dependent stability analysis, stabilization,gain-scheduled control and model reduction for LPV systems with state delays in terms of parameterized linear matrix inequalities(PLMIs).Firstly,based on different parameter-dependent Lyapunov-Krasovskii functions,new parameter-dependent and delay-dependent stability criteria are proposed for LPV systems with a time-varying state delay in both continuous-and discrete-time cases.It shows that the stability conditions proposed in this thesis are much less conservative than the reported results.Secondly,the problems of state feedback stabilization and H_∞control are addressed for LPV systems with a time-varying state delay in both continuous-and discrete-time cases. Based on the stability conditions obtained in this thesis,sufficient conditions are proposed for designing delay-dependent gain-scheduling stabilization controllers and H_∞state feedback gain-scheduling controllers,upon which can convert the existence condition of admissible controllers into the feasibility of convex problems subject to linear matrix inequalities.The numerical examples show that the proposed approach is less conservative.Thirdly,the problems of state observer-based output-feedback stabilization and H_∞control are considered for LPV systems with a time-varying state delay in both continuous-and discrete-time systems.The observer-based delay-dependent gain-scheduling controllers and H_∞controller are designed respectively.The H_∞gain-scheduling controller and observer can guarantee that the resulting closed-loop system is asymptotically stable and has an adequate desired H_∞performance level.The efficiency and feasibility of the proposed technique are further demonstrated by numerical examples.Finally,the problems of H_∞model reduction for time-delayed LPV continuous-and discrete-time systems are presented.Based on the parameter-dependent Lyapunov stability idea,the methods are presented for constructing a reduced-order time-delayed LPV system to approximate a given time-delayed LPV system with guaranteed H_∞error performance using congruence transformations and matrix variable changes.And numerical examples show the feasibility and applicability.