Ellipsoidal set-theoretic approach for stability of linear state-space models with interval uncertainty

This paper addresses the issue of conservatism in the stability robustness bound obtained by the Lyapunov matrix equation solution. Ellipsoidal set-th eoretical approach is employed to improve the bound on the interval uncerta inty of an asymptotically stable linear system for robust stability. The fo rmula of determination of the ellipsoid from the given interval uncertainti es is given in this paper. The improved bound is obtained, using ellipsoida l set-theoretical approach, on vector uncertainties (i.e. structured uncert ainty) as well as on a matrix uncertainties (i.e. unstructured uncertainty) . The bound is shown to be less conservative than that obtained by the inte rval set-theoretical approach. Examples given include comparison of the ell ipsoidal set-theoretical approach with the interval set-theoretical approac h. (C) 2001 IMACS. Published by Elsevier Science B.V. All rights reserved.