On Sliding Mode Control for Singular Fractional-Order Systems with Matched External Disturbances

Abstract

In this paper, we investigate the problem of sliding mode control for singular fractional-order systems that have matched uncertainties. We design an innovative integral sliding mode function and controller based on the normalizable condition. A strict linear matrix inequality-based sufficient condition is obtained for the system’s stability. The normalizable condition is eliminated by updating and developing the control method, and a sufficient and necessary condition is developed for the admissibility of the system. Lastly, verification of our method’s effectiveness is numerically conducted in two instances.

Sliding Mode Control for a Class of Nonlinear Fractional Order Systems with a Fractional Fixed-Time Reaching Law

“…With sliding mode controller (20), one can obtain that ṡi The following analysis is established for each control input u i in (20); thus, we only analyze the properties for a single input. The subscript i in (20) and ( 21) is omitted for convenience in the following discussion.…”

“…In [17], the authors discuss the problem of tracking and stabilization of a class of chained fractionalorder nonlinear systems via SMC with a single input. SMC is used to realize the stabilization and synchronization of fractional chaotic systems [18][19][20][21]. For instance, in [22], SMC with an adaptive reaching law is presented to control a class of fractional chaotic systems, including fractional Lure systems, fractional Lorenz systems, and so on.…”

Generalized Criteria for Admissibility of Singular Fractional Order Systems

“…Ref. [24] gave three different criteria for the admissibility and stabilization of SFOSs when the differential order is in the interval 0 < α < 1, which promoted the research [25,26] on related problems of SFOSs to some extent. The admissibility of SFOSs is still a hot topic in the field of control.…”