Robust Control of Polytopic Systems by Convex Optimization

Robust control synthesis of linear time-invariant SISO polytopic systems is investigated using the polynomial approach. A convex set of all stabilizing controllers for a polytopic system is given over an infinite-dimensional space. A finite-dimensional approximation of this set is obtained using the orthonormal basis functions and represented by a set of LMIs thanks to the KYP Lemma. Then, an LMI based convex optimization problem for robust pole placement with sensitivity function shaping in two- and infinity-norm is proposed. The simulation results show the effectiveness of the proposed method.

Published in:
Automatica, 43, 6, 1395-1402
Year:
2007
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