Robust H∞ control for uncertain linear time invariant descriptor systems

The H_∞ control problem for uncertain descriptor systems with time-invariant nonbound uncertainty in the state matrix is considered. Necessary and sufficient conditions for robust H_∞ control of descriptor systems by state feedback and dynamic output feedback are derived. The design results are expressed in terms of generalised algebraic Riccati inequalities, which may be considered an extension of results given in recent literature. Explicit formulae for controllers which solve the corresponding problems are provided. The generalised algebraic Riccati inequalities approach used is based on a version of the bounded real lemma for descriptor systems, thus making the given proofs simpler