Finite-time reliable nonfragile control for fractionalorder nonlinear systems with asymmetrical saturation and structured uncertainties

Abstract

This paper investigates the finite-time stabilization problem of fractional-order nonlinear differential systems via an asymmetrically saturated reliable control in the sense of Caputo’s fractional derivative. In particular, an asymmetrical saturation control problem is converted to a symmetrical saturation control problem by using a linear matrix inequality framework criterion to achieve the essential results. Specifically, in this paper, we obtain two sets of sufficient conditions under different scenarios of structured uncertainty, namely, norm-bounded parametric uncertainty and linear fractional transformation uncertainty. The uncertainty considered in this paper is a combination of polytopic form and structured form. With the help of control theories of fractional-order system and linear matrix inequality technique, some sufficient criteria to ensure reliable finite-time stability of fractional-order differential systems by using the indirect Lyapunov approach are derived. As a final point, the derived criteria are numerically validated by means of examples based on financial fractional-order differential system and permanent magnet synchronous motor chaotic fractional-order differential system.

Keywords

• fractional-order differential system
• reliable nonfragile controller
• finite-time control
• asymmetric input saturation
• structured uncertainty