Robust Control Design of Uncertain Discrete-Time Descriptor Systems with Delays

A descriptor system describes a natural representation for physical systems. In general, the continuous-time descriptor representation consists of differential and algebraic equations, and the discrete-time descriptor system has difference and algebraic equations. Hence, the descriptor system is a generalized representation of the state-space system. This system appears in various physical systems. In fact, descriptor systems can be found in electrical circuits, moving robots and many other practical systems which are modeled with additional algebraic constraints. The descriptor system is also referred to as singular system, implicit system, generalized state-space system, differential-algebraic system, or semistate system. System analysis and control design of descriptor systems have been extensively investigated in the past years due to their potential representation ([4], [6], [7], [17], [23]). An important characteristic of continuous-time descriptor systems is the possible impulse modes, which are harmful to physical systems and are undesirable in system control. The discrete-time descriptor system may not have causality, which leads to no solution of the system states. In [4], [32], such descriptor system behaviors are described and notion of regularity, non-impulse, causality, and admissibility are given. In [1] and [22], quadratic stability for continuous-time descriptor systems was considered. Its discrete-time system counterpart was investigated in [31] and [32].