Resilient Guaranteed Cost Control For Uncertain Singular Time-delay Systems: Delay Decomposition Approach

This thesis considers the problem of state feedback resilient guaranteed cost con-troller design for singular time-delay systems with norm-bounded parameter uncer-tainty. The whole thesis is divided into three sections.Chapter 1 is the introduction. This section includes some results in the past years, which were known by writer. And it points out the meaning of researching in this thesis.Chapter 2 is system formulation and preliminaries. We consider a class of uncer-tain singular time-delay system represented by where x(t)∈Rn,u(t)∈Rq are the state and control input, respectively. E, A, AT and B are known real constant matrices with appropriate dimensions and 0< rankE= p<n.τis an unknown constant delay and satisfies 0<τ<τm≤τm.φ(t)∈Cn,τis a compatible initial function.ΔA andΔAτare time-invariant matrices representing norm-bounded parametric uncertainties which arc of the following form: where D1,E1, ET are known real constant matrices and F1 is an uncertain real con-stant matrix. Given positive definite symmetric matrices R and S, we consider the cost functionalThe object is to design a resilient guaranteed cost controller u(t)= (K+ΔK)x(t),K∈Rm×n, K is a constant matrix, such that for all admissible uncer-tainties, the closed-loop system is regular, impulse free, asymptotically stable and the closed-loop value of the cost functional J satisfies a bound J*. We focus on the resilient controllers respect to additive and multiplicative controller gain variations. It is well known that in practical engineering, the controller is not easy to be precise or exactly implemented, but has a certain degree of errors. Hence, it is considered beneficial that the design of delay-dependent robust resilient controller for uncertain singular time-delay systems.A new approach-delay decomposition approach [19] is proposed to deal with the problem [19]. The idea of the approach is that the delay interval is uniformly di-vided into N segments with N a positive integer, and a proper Lyapunov-Krasovskii functional is chosen with different weighted matrices corresponding to different seg-ments in the Lyapunov-Krasovskii functional. For singular time-delay systems, [20] constructs a new Lyapunov-Krasovskii functional: where, PE=ETPT> 0.Chapter 3 is the main work of this thesis. In this section, we give delay-dependent sufficient conditions for the existence of the state feedback resilient guaranteed cost controllers based on the new Lyapunov-Krasovskii functional (0.8), which are pre-sented in Theorem 2 and Theorem 3. In addition, in order to solve the problem by using the Matlab toolbox, we convert the matrix inequalities in Theorem 2 and Theorem 3 to the form of linear matrix inequalities.