Connections between stability conditions for slowly time-varying and switched linear systems

Abstract— This paper establishes an explicit relationship between stability conditions for slowly time-varying linear systems and switched linear systems. The concept of total variation of a matrix-valued function is introduced to characterize the variation of the system matrix. Using this concept, a result generalizing existing stability conditions for slowly time-varying linear systems is derived. As a special case of this result, it is shown that a switched linear system is globally exponentially stable if the average dwell time of the switching signal is large enough, which qualitatively matches known results in the literature.

• Type: Journal
• Year: 2015
• Where: CDC
• Authors: Xiaobin Gao, Daniel Liberzon, Ji Liu 0001, Tamer Basar
• Keywords: CDC 2015, Control Systems