ON THE STABILITY RADIUS OF A GENERALIZED STATE-SPACE SYSTEM

The concept of ''distance to instability'' of a system matrix is gener alized to system pencils which arise in descriptor (semistate) systems . Difficulties arise in the case of singular systems, because the penc il can be made unstable by an infinitesimal perturbation. It is necess ary to measure the distance subject to restricted, or structured, pert urbations. In this paper a suitable measure for the stability radius o f a generalized state-space system is defined, and a computable expres sion for the distance to instability is derived for regular pencils of index less than or equal to one. For systems which are strongly contr ollable it is shown that this measure is related to the sensitivity of the poles of the system over all feedback matrices assigning the pole s.