Regional Stability and Stability Radius*

Abstract

In this work we consider the problem of stability, for distributed parameter systems, through the space variable. We give an extension of the stability radius, introduced by A. J. Pritchard and S. Townley [7, 10], to the regional case. This consists to determine the “smallest disturbance” which destabilizes regionally an exponentially stable system. We prove in particular that for a certain given class of distributed parameter systems, it is possible to destabilize regionally an exponential stable system without destabilizing it totally.