ABSTRACT
Discrete-time singularly perturbed control systems have been the subject of intensive research since the early 1980s. Several researchers have produced important results on different aspects of control problems of deterministic singularly perturbed discrete-time systems such as Phillips, Blankenship, Mahmoud, Sawan, Khorasani, Naidu and their coworkers. Particularly important are the fundamental results of Khalil and Litkouhi, (Litkouhi, 1983; Litkouhi and Khalil, 1984, 1985). Along the lines of the research of Khalil and Litkouhi, in (Gajic and Shen, 1991a, b) an extension of the linear-quadratic optimal control problem of (Litkouhi and Khalil, 1984) and the formulation and the solution of the linear-quadratic Gaussian stochastic control problem are presented.
