On the stability radius of a generalized state-space system

Byers, R. and Nichols, N. ORCID: https://orcid.org/0000-0003-1133-5220 (1993) On the stability radius of a generalized state-space system. Linear Algebra and its Applications, 188-189. p. 113. ISSN 0024-3795 doi: 10.1016/0024-3795(93)90466-2

Abstract/Summary

The concept of “distance to instability” of a system matrix is generalized to system pencils which arise in descriptor (semistate) systems. Difficulties arise in the case of singular systems, because the pencil can be made unstable by an infinitesimal perturbation. It is necessary to measure the distance subject to restricted, or structured, perturbations. In this paper a suitable measure for the stability radius of a generalized state-space system is defined, and a computable expression for the distance to instability is derived for regular pencils of index less than or equal to one. For systems which are strongly controllable it is shown that this measure is related to the sensitivity of the poles of the system over all feedback matrices assigning the poles.