Abstract
In this paper we consider the H∞ control problem for a plant possessing zeros at infinity. Namely it is not assumed that direct-feedthrough matrices are of full rank. A necessary and sufficient condition is derived for the solution to exit. It depends on the solvability of two generalized Riccati equations. An algorithm is proposed with which the generalized Riccati equations can be solved by reducing them into usual Riccati equations. A parametrization is given for all compensators that are not necessarily proper. Also the existence of the proper compensator is proved. We use the properties of J-lossless matrix and the descriptor form representation to solve the problem.
