On mean-square-stable bilinear systems
O.L.V. Costa, GISELLE M. S. FERREIRA, Carlos S. Kubrusly · IMA Journal of Mathematical Control and Information · 1995
It has been shown in a previous paper that an infinite-dimensional stochastic discrete bilinear system is mean-square-stable if and only if the spectral radii of two transformations of Hilbert-space operators are both less than one. The present paper investigates conditions to be imposed on the model operators in order to ensure that such spectral radii coincide. Several examples are presented and the main result establishes the spectral radius identity for models with compact operators.