The authors present a study of the H-infinity control problem and related topics for descriptor systems, described by a set of nonlinear differential-algebraic equations. They derive necessary and sufficient conditions for the existence of a controller solving the standard nonlinear H-infinity control problem considering both state feedback and output feedback. One such condition for the output feedback control problem to be solvable is obtained in terms of two Hamilton–Jacobi inequalities and a weak coupling condition; a parameterization of a family of output feedback controllers solving the problem is also provided. All of the aforementioned results are then specialized to the linear case.

For the linear case, the necessary and sufficient conditions for the corresponding problems to be solvable are expressed in terms of two hierarchically coupled generalized algebraic Riccati equations. When these conditions hold, state-space formulae for a controller solving the problem are also given. The approach used in this monograph is based on a generalized version of the Bounded Real Lemma. Finally, the derivation of state-space formulae for all controllers solving the standard H-infinity control problem for descriptor systems is proposed. To establish the key formulae, a parameterization of all internally stabilizing controllers for descriptor systems is also given (both the linear and nonlinear cases are considered in this monograph). Among other important topics to be investigated are the balanced realization, reduced-order controller design and mixed H₂/H-infinity control problems.

For students and researchers interested in nonlinear control theory for descriptor systems, this book provides both a comprehensive introduction and easy access to advanced topics.