$\mathcal{H}_\infty$ Control for Nonlinear Descriptor Systems / by He-Sheng Wang, Chee-Fai Yung, Fan-Ren Chang.

Springer eBooks

Introduction -- Elements of Descriptor Systems Theory -- Youla Parameterization -- The H-infinity Control -- Balanced Realization -- Some Further Topics -- Conclusions -- Appendices: Generalized Algebraic Riccati Equations; Center Manifold Theory.

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 and output feedback. One such condition for the output feedback control problem to be solvable is obtained in terms of Hamilton–Jacobi inequalities and a weak coupling condition; a parameterization of output feedback controllers solving the problem is also provided. All of these results are then specialized to the linear case. The derivation of state-space formulae for all controllers solving the standard H-infinity control problem for descriptor systems is proposed. Among other important topics covered are balanced realization, reduced-order controller design and mixed H2/H-infinity control. "H-infinity Control for Nonlinear Descriptor Systems" provides a comprehensive introduction and easy access to advanced topics.

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