A study of the generalized input-to-state ℒ2-gain of discrete-time switched linear systems

A generalized notion of the input-to-state L₂-gains of discrete-time switched linear systems is proposed in this paper. Such gains are then characterized using the radii of convergence of a family of suitably defined functions called the generating functions. Properties of the generating functions are studied and their numerical computation algorithms are developed. Some numerical examples are presented.