On the computation of dwell time using the real Jordan form

This paper addresses the question of guaranteeing stability for a switching system. For this work, a switching system consists of a collection of subsystems with known LTI models and a switching signal that determines which subsystem model governs the system´s dynamics at any given time. The switching signal may be the result of an operator´s choice or a reaction to external events. Previous work has shown that the switching system will be stable if the switching signal is piecewise constant and dwells on each chosen value for some minimum period of time. Morse and Geromel have proposed methods for estimating an upper bound on the minimum dwell time from the realizations of the LTI subsystems. The new approach proposed in this paper utilizes the real Jordan form and produces a much more accurate estimate than Morse while requiring significantly fewer computations than Geromel. Numerical simulation of a switched system derived from an adaptive vibration attenuation controller illustrates the accuracy and computational efficiency of the proposed algorithm.