Input‐output finite‐time stability of fractional‐order switched singular continuous‐time systems

Abstract

The input‐output finite‐time stability and stabilization of a class of fractional‐order switched singular continuous‐time systems with order 0<α<1 are studied in this paper. First, based on the average dwell time switching technique, by constructing multiple Lyapunov functions, the sufficient conditions of input‐output finite‐time stability for the considered systems are derived in the form of linear matrix inequalities (LMIs). Second, a suitable LMI‐based state feedback controller is designed. Finally, an illustrative example is presented to show the effectiveness of the proposed technique.

Guaranteed cost and finite-time event-triggered control of fractional-order switched systems

“…In addition, there have been also some results about FOSS (e.g. Feng et al, 2019a, Feng et al, 2019bLiang et al, 2019b;Liu et al, 2018a).…”

Event‐triggered H∞ control of discrete‐time switched linear systems with delays

“…Delays and disturbances are inevitable in practical engineering. Delays make the analysis and synthesis of systems more complicated [8–10], and disturbances are generally detrimental to system performance [11]. The most frequently used method for dealing with stability of delayed systems is Lyapunov–Krasovskii functional method [12–14], and $$$ {H}_{\infty } $$$ control is often employed to investigate dynamics of systems with disturbances.…”

Stabilization for nonlinear fractional‐order time‐varying switched systems

“…And in Sakthivel et al [13], the tracking problem was discussed for positive FOSS via the Lyapunov stability theory and average dwell time (ADT) scheme. Feng et al [14] investigated the input-output finite-time stability of singular FOSS. Nevertheless, there are few researches on fractional-order time-varying systems.…”

“…The dynamics of fractional-order systems under the switching control strategies can also be modeled as fractional-order switched systems (FOSS). Very recently, fruitful advance about FOSS has been proposed in earlier studies [11][12][13][14][15] and references therein. Such as the sufficient stability conditions of FOSS in the presence of impulsive and time delays were derived in He and Xu [12] by utilizing mode-dependent average dwell time (MDADT) method.…”