Research On Resilient Guaranteed Cost Control For Time-Delay Systems

Recently, the problem of designing robust controllers to make uncertain systems not only be stable but also guarantees an adequate level of performance has drawn considerable attention. One approach to this problem is the guaranteed cost control approach first introduced by Chang and Peng.This approach is to design a controller such that the closed-loop system is asymptotically stable for all admissible uncertainties and the closed-loop cost function value is not more than a specified upper bound.It is well known that time-delays as well as parameter uncertainties are frequently the main cause of deterioration of systems performance and instability of systems.Therefore, there has been increasing interest in the guaranteed cost control of uncertain time-delay systems,and many significant results have been presented.However, there have been few results for nonlinear systems, owing to their partieularity and compexity.Based on, the Lyapunov stability theory and linear matrix inequality approach, the problems of guaranteed control for nonlinear time-delay systems with norm-bounded uncertainties are considered.The main contents in this paper are as follows:Firstly, a condition for the existence of resilient guaranteed cost controller is derived via linear matrix inequalities (LMI) technology and Lyapunov function. Designing methodology and conditions of existence in resilient guaranteed cost control is diseussed for uncertain nonlinear time-delay systems under two classes of controller gain perturbations, namely, additive form and multiplicative form. Solving a convex optimization problem gives the optimal guaranteed cost value of the system.Secondly, a condition for the existence of resilient guaranteed cost controller is derived via linear matrix inequalities (LMI) technology. To be regular, impulse- free and robustly stable for all admissible uncertainties and conditions of existence in resilient guaranteed cost control for singular systems with time varying interval time-delay is given. Furthermore, it is shown that this condition is equivalent to the feasibility problem of LMIs, and its solutions provide a parameterized representation of resilient guaranteed cost controllers.Thirdly, In terms of linear matrix inequalities (LMIs), a design method is obtained by constructing generalized Lyapunov function and generalized quadratic regulator.The last section summarizes the main work in this paper and prospects the research of uncertain guaranteed cost control problems in the future.