Abstract: The stabilization problem of systems that switch among a finite set of slowly varying linear systems with arbitrary switching frequency is discussed. It is shown that if the entries of the pointwise stabilizing feedback gain matrix are continuously differentiable functions of the entries of the system coefficient matrices, then the closed-loop system is uniformly asymptotically stable if the rate of time variation of the system coefficient matrices is sufficiently small.

Key words: slowly varying, switched linear systems, stabilization, frozen-time method; stability