International Federation of Automatic Control
3rd IFAC SYMPOSIUM on SYSTEM, STRUCTURE and CONTROL
Foz do Iguassu, Brazil October 17th - 19th, 2007
| International Federation of Automatic Control | |
Session FE1: Robust Control IIChair: Shinji Hara - Japan Co-chair: Shankar Bhattacharyya - United States Room: Assunção 2007-10-19 From 16:00 to 18:00 | |
| LMI Relaxations for H∞ Control of Time-Varying Polytopic Systems by Means of Parameter-Dependent Quadratically Stabilizing Gains R. C. L. F. Oliveira; V. F. Montagner; P. L. D. Peres; P. -A. Bliman Contact: Pedro L. D. Peres - Brazil | |
| 16:40-17:00 | |
| Abstract: | |
| This paper provides necessary and sufficient conditions in terms of LMI relaxations to compute H∞ parameter-dependent state feedback control gains that ensure closed-loop quadratic stability for linear systems affected by arbitrarily fast time-varying parameters inside a polytope. The proposed conditions, based on an extension of Pólya's Theorem and on the systematic construction of homogeneous polynomial solutions for parameter-dependent linear matrix inequalities, are written as a sequence of progressively less and less conservative linear matrix inequality conditions. Necessity is attained as the level of relaxation increases, providing an H∞ parameter-dependent state feedback gain that quadratically stabilizes the system whenever such a gain exists. An extension to compute decentralized control gains is also presented and numerical results illustrate the efficiency of the proposed conditions. Copyright © 2007 IFAC. | |