H∞-control of differential-algebraic-equation systems

Ansgar Rehm & Frank Allgöwer
In this paper H∞ control of high index and non-regular linear differential-algebraic-equation systems is addressed. Based on a generalization of the bounded real lemma (BRL) to index one systems, all linear output feedback controllers in standard, ie non-descriptor, state space form solving the H∞ control problem can be characterized via biaffine matrix inequalities (BMIs). In a second step a congruence transformation and a subsequent change of variables show that certain linear matrix inequalities (LMIs) necessarily...
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