Abstract
In this paper H∞ control of high index and non-regular linear differential-algebraic-equation systems are addressed. Based on a generalization of the bounded real lemma (BRL) to index one systems, all controllers solving the H∞ control problem can be characterized via biaffine matrix inequalities (BMIs). A subsequent linearizing change of variables leads to certain linear matrix inequalities (LMIs) which are shown to be necessary for the existence of a linear output feedback controller in standard, i.e. non-descriptor, state space description. From these necessary conditions non-conservative sufficient conditions can be derived as BMIs of reduced order compared to the original characterization via the bounded real lemma. The approach is illustrated by a simple example.
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