Discrete-time H _∞ Almost Disturbance Decoupling

Abstract

In this chapter, we consider the problem of H _∞ almost disturbance decou­pling for general discrete-time plants whose subsystems are allowed to have invariant zeros on the unit circle of the complex plane. The stability region of a discrete-time system considered in this chapter is defined as usual as the open unit disc. In contrast to the continuous-time case, the problem of almost disturbance decoupling for general discrete-time systems is less studied in the literature. In 1996, Chen, Guo and Lin [17] gave a set of solvability conditions for the H _∞-ADDPMS for the special case when a given plant whose subsys­tems do not have invariant zeros on the unit circle. Only very recently, has the necessary and sufficient conditions under which the H _∞-ADDPMS for general discrete-time systems been derived by Chen, He and Chen [18]. Solutions to such a general problem have just been reported by Lin and Chen [65]. The results of [18] and [65] form the core of this chapter.