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Rank-one LMI approach to simultaneous stabilization of linear systems

✍ Scribed by Didier Henrion; Sophie Tarbouriech; Michael Šebek

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
110 KB
Volume
38
Category
Article
ISSN
0167-6911

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✦ Synopsis

Following a polynomial approach to control design, the simultaneous stabilization by a controller of given ÿxed order of a family of SISO linear systems is interpreted as an NP-hard BMI feasibility problem. Upon formulating this BMI problem as an LMI problem with an additional non-convex rank constraint, two simultaneous stabilization methods are then proposed. The ÿrst method is a heuristic algorithm performing rank minimization by potential reduction. The second method hinges upon necessary conditions and su cient conditions for simultaneous stabilization derived from geometric properties of the intersection of a set of ellipsoids. Both methods are then illustrated by numerical examples.

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