Stabilizability and lower spectral radius for linear switched systems with singular matrices

Abstract

We investigate the stabilizability of linear discrete-time switched systems with singular matrices, focusing on the spectral radius in this context. A new lower bound of the stabilizability radius is proposed, which is applicable to any matrix set. Switched systems with rank one singular matrices are discussed: The stabilizability radius and the joint spectral subradius are equal for such systems. Detailed analysis of the stabilizability radius of two-dimensional switched systems, consisting of a singular matrix and a matrix with complex eigenvalues or real eigenvalues, are presented. The condition when an infinitely long aperiodic optimal sequence appears of such system is also discussed. Other properties of switched systems with singular matrices are also discussed along with examples

Version 4: Clarified and substantially expanded