Positive polynomials and robust stabilization with fixed-order controllers

• Published in: IEEE transactions on automatic control Vol. 48; no. 7; pp. 1178 - 1186
• Main Authors: Henrion, D., Sebek, M., Kucera, V.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.07.2003; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Aerospace industry; Applied sciences; Approximation; Associate members; Computer science; control theory; systems; Control systems; Control theory. Systems; Controllers; Design engineering; Design optimization; Exact sciences and technology; Ingredients; Linear matrix inequalities; Linear systems; Mathematical analysis; Miscellaneous; Optimization; Polynomials; Robust control; Robust stability; Stability; Uncertainty; Robust control; Polynomial; Polytope; Uncertainty; Uncertain system; Approximation; Linear system; Stabilization; Linear matrix inequality; Numerical method; Inner; Optimization
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2003.814103

Recent results on positive polynomials are used to obtain a convex inner approximation of the stability domain in the space of coefficients of a polynomial. An application to the design of fixed-order controllers robustly stabilizing a linear system subject to polytopic uncertainty is then proposed, based on linear matrix inequality optimization. The key ingredient in the design procedure resides in the choice of the central polynomial. Several numerical examples illustrate the relevance of the approach.