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

In this paper, some useful properties of generalized algebraic Riccati equa tions 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 descriptor systems. Necessary an d sufficient conditions are derived for the solution to this problem expres sed in terms of two generalized algebraic Riccati equations which may be co nsidered to be generalizations of the Riccati equations obtained by Sun et al. (1994). When these conditions hold, state space formulae for all contro llers solving the problem are also given.