The singular linear-quadratic optimal control problem for a class of discrete-time linear singular systems with multiple time-delays is investigated. The equivalent relationship between this problem and the non-singular linear-quadratic problem for standard state-space discrete-time linear systems without time-delay is derived, and the necessary and sufficient condition guaranteeing this equivalent relationship is also given. The optimal control is synthesized as state feedback, and the closed-loop system is regular, impulse-free and without time-delay. An example is given to show the validity of the proposed method.

This paper investigates the problem of semiglobal L2 disturbance attenuation for a class of nonlinear systems. By [4], our purpose of designing controllers is just to attenuate all disturbances in a given bounded subset of L2 [0, ∞]. We prove that for any such a given bounded subset there exist partial state feedbacks and dynamic output feedbacks respectively which attenuate each disturbance in the given bounded subset in the L2 gain sense and attain asymptotic stability without disturbance.

The robust output feedback stabilization problem for singular time delay system with norm-bounded parametric uncertainties is considered in this paper. All the coefficient matrices except the matrix E include uncertainties. The authors derive sufficient conditions about the robust stability of the two closed-loop systems which are obtained by applying an observer-based controller and a compensator to the singular time delay system respectively. Then the strict linear inequality (LMI) design approaches are developed and the desired robust output feedback control laws are given.

A necessary and sufficient condition for the output regulation problem to be solvable by output feedback reducedorder normal controllers is derived, which can be constructed explicitly.

Three kinds of observers for linear singular time delay systems, namely functional observers, reduced-order obsevers and full-order observers, are considered iu this paper. About the former two, observers with and without internal delay are considered respectively. About the latter, observers without internal delay is given. The corresponding design steps for various observers, which are all nolrmal linear time delay systems, are presented. Numerical examples are given to illustrate the methods.