Stability robustness bounds for linear state-space models with structured uncertainty based on ellipsoidal set-theoretic approach

This paper is concerned with the problem of robust stability of linear dyna mic systems with structured uncertainty by means of ellipsoidal set-theoret ic approach. In this paper, the uncertainty in the physical parameters is e xpressed in terms of an ellipsoidal set in appropriate vector space. Two el lipsoidal set-theoretic approaches are presented for giving sufficient cond itions for robust stability property of the systems with structured uncerta inty. The bound produced by the ellipsoidal extension function theorem is s hown to be less conservative than the one predicted by the La,orange multip lier method. In order to introduce the ellipsoidal extension function theor em, in Appendix A of this paper, we try to present the theory of ellipsoida l algebra, following the thought of interval analysis. First of all, we giv e the concept of ellipsoidal numbers and define their arithmetic operations . Based on them, we finally introduce ellipsoidal vectors and ellipsoidal f unctions. In terms of the inclusion monotonic property of ellipsoidal funct ions, we present and prove the ellipsoidal extension function theorem. (C) 2001 IMACS. Published by Elsevier Science B.V. All rights reserved.