The positive real control problem and the generalized algebraic Riccati equation for descriptor systems

Abstract

In this paper, some useful properties of generalized algebraic Riccati equations and generalized positive real lemma for descriptor systems are given. Based on these results, the main purpose of this paper is to investigate the positive real (PR) control problem for de-scriptor systems. Necessary and sufficient conditions are derived for the solution to this problem expressed in terms of two generalized al-gebraic Riccati equations which may be considered to be generaliza-tions of the Riccati equations obtained by Sun et al. (1994). When these conditions hold, state space formulae for all controllers solving the problem are also given.