Contents I. Introduction
In the literature, quite a few results on how to make a control design by state feedback controllers have been addressed. A controller with the state feedback is simple, but, in physical systems, not every state variable of the system is usually feasible for the feedback. Hence, the output feedback controller design is a crucial problem for physical systems. In modeling physical systems, a descriptor system plays an important role. A descriptor system is a general representation which is composed with differential equations and algebraic equations, and hence it can express a dynamical system with algebraic constraints, and can generalize an ordinary state-space system. In fact, a descriptor system is adopted in most engineering and scientific fields as mobile robots, mechanical systems and etc. The descriptor model is also called generalized state-space model, implicit model, differential-algebraic model, singular model, or semistate model. Due to its importance, many works on control synthesis and system analysis of descriptor systems have been made([2], [10], [7]). One of the crucial features of descriptor systems is the impulsive mode, which is undesirable in controlling descriptor systems. In [2] and [23], system behaviours of such descriptor systems are explained and definitions of regularity, impulsive modes, and admissibility are clarified. In [22], admissibility for discrete-time descriptor systems was studied. The continuous-time case was done in [9]. Furthermore, various problems on system analysis and synthesis for descriptor systems were investigated in [4], [21] and [23], and various design methods of admissible controllers were obtained there.
