On the computation of dwell time using the real Jordan form

Abstract

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.

An anti-windup scheme for an adaptive &#x210B;<inf>&#x221E;</inf> vibration controller: Development and simulations

“…It is emphasized that the results derived are distinct from those presented in [15] (and subsequent work) for indirect adaptive control schemes. [4]. The challenge considered in this paper is the design of an anti-windup compensator, Θ, which is able to maintain, to some extent, the disturbance rejection capabilities of the controller when saturation is present.…”

“…The main idea of [1], [3] is to design a baseline robust controller and a set of so-called single frequency controllers which are switched in and out as needed to provide optimal disturbance rejection. Effectively, the adaptive robust controller is a switched controller with the switch depending on the disturbance profile [4]. Both simulation and practical results have revealed that this technique can offer extremely good disturbance rejection capabilities [5].…”