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

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. Based on this lower bound, more relationships between the stabilizability radius and joint spectral subradius are established. Detailed analysis of the stabilizability radius of a special kind of two-dimensional switched system, consisting of a singular matrix and a rotation matrix, is presented. The Hausdorff dimensions of the parameter sets such that the stabilizability radius of these systems equals a constant are also presented. Other properties of switched systems with singular matrices are also discussed along with examples.