In this paper, we present the theoretical development to stabilize a class of uncertain time-delay system. The system under consideration is described in state space model containing distributed delay, uncertain parameters and disturbance. The main idea is to transform the system state into an equivalent one, which is easier to analyze its behavior and stability. Then, a computational method of robust controller design is presented in two parts. The first part is based on solving a Riccati equation arising in the optimal control theory. In the second part, the finite dimensional Lyapunov min-max approach is employed to cope with the uncertainties. Finally, we show how the resulting control law ensures asymptotic stability of the overall system.

The robust finite settling time stabilization problem is considered for a multivariable discrete time plant with structured uncertainties. Finite settling time (FST) stability of a feedback system is a notion introduced recently for discrete time systems as a generalization of the dead-beat response. The uncertain plant treated in this paper is described by (E0+ΣKi=1qiEi)x(t+1)(A0+ΣKi=1qiAi)x(t)+(B0+ΣKi=1qiBi)u(t), and y(t)=(C0+ΣKi=1qiCi)x(t) where Ei, Ai, Bi and Ci (0iK) are prescribed real matrices and qi (1iK) are uncertain parameters restricted to prescribed intervals [qi, i]. It is shown in this paper that a controller robustly FST stabilizes such an uncertain plant, if, the uncertain plant satisfies some conditions, and the controller simultaneously FST stabilizes a finite set of plants. The result leads to a testable necessary and sufficient condition of the existence of a solution to the robust FST stabilization problem, and a systematic method of designing a robust FST stable feedback system, in the case where the plant contains only one uncertain parameter.