Rehm, AnsgarAllgöwer, Frank1999-06-152016-03-311999-06-152016-03-311998070842450http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-3534http://elib.uni-stuttgart.de/handle/11682/6917http://dx.doi.org/10.18419/opus-6900In 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 must hold in order to admit a solution of the H∞ control problem. However, these conditions are not sufficient. Necessary and sufficient conditions for the existence of a controller solving the H∞ control problem are derived as BMIs of reduced order compared to the original characterization via the BRL. The approach is illustrated by a simple example.eninfo:eu-repo/semantics/openAccessDifferential-algebraisches Gleichungssystem , Regelung660Bounded Real LemmaBounded Real Lemma , descriptor systems , controlreport2015-11-11