Singular Time-delay Systems Of Fragile Reliable Guaranteed Cost Control And Its Control

Time delays usually make the systems uncertain and the controller design more difficult. Consequently, the study of this kind of systems has attracted considerable attention in the last decades.In the research of the robust control of uncertain systems, a controller is usually designed such that the uncertain system is robustly stable and has an adequate level of performance. To this end, the guaranteed cost control is presented. The main idea of the guaranteed cost control is to design a controller such that the closed-loop system is asymptotically stable and a corresponding upper bound of the closed-loop cost function value is obtained for all admissible uncertainties.The system we study in this paper can be described as follows where E∈Rn×n, rank(E)=r<n, x(t)∈Rn, called the state, u(t)∈Rm, called the control input, A, A1, B,B1, D are known appropriate real matrices, ΔA, ΔA1, ΔB, ΔB1represent norm-bounded parameter uncertainties,0≤d(t)≤d<∞,0≤h(t)≤h<∞are time-varying delays, and φ(t) is the initial function.For this class of time-delay systems, this paper focuses on the problem of the non-fragile guaranteed cost control and it’s non-fragile reliable guaranteed cost con-trol. A design procedure of a non-fragile controller is given based on the Lyapunov stability theory and LMI approach.The main conclusions in this paper are as follows:(1) A method for designing a non-fragile guaranteed cost controller is given in terms of LMI approach. Sufficient conditions for the existence of the non-fragile control law are presented such that the closed-loop system is asymptotically stable and a corresponding upper bound of the closed-loop cost function value is obtained for all admissible uncertainties. A numerical example illustrates the feasibility of the proposed approach. (2) Based on the LMI approach, the problem of designing a non-fragile reliable guaranteed cost controller is solved. The given sufficient conditions ensure the exis-tence of the non-fragile control law. A numerical example illustrates the feasibility of the proposed approach.