Robust asymptotic stability of 2-D shift-variant discrete state-space systems

Abstract

The results described in this paper provide conditions for the asymptotic stability of 2-D shift-variant uncertain systems expressed using the Roesser state-space description. A necessary and sufficient condition for the asymptotic stability of 1-D systems involves checking all products of extreme matrices. The same test is shown to apply to 2-D systems, although the corresponding stability condition is sufficient, but not necessary.