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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