Finite-Time Synchronization of Coupled Fractional-Order Systems via Intermittent IT-2 Fuzzy Control

Abstract

Considering the memory property of the fractional calculus and the potential diverging state of the open-loop mode, existing analysis methods are difficult to solve the finite-time issue of intermittently controlled fractional-order systems (FOSs). This article studies the finite-time synchronization of coupled FOSs with nonlinearity via fuzzy intermittent quantized control and two novel fractional-order differential inequalities. An interval-type 2 Takagi-Sugeno fuzzy technique is introduced, which not only facilitates the handling of the nonlinear term in the error dynamic system, but also greatly simplifies the control design. Synchronization conditions in form of linear matrix inequalities are provided by designing a novel Lyapunov function on the basis of ellipsoidal norm. Moreover, two corollaries show the generality of the new analysis framework. Compared with existing results, it is amazing that the decreasing magnitude of Lyapunov function on the control intervals can be smaller than its increasing magnitude on the subsequent noncontrol interval. Finally, Chua’s system is used to clarify the effectiveness of theoretical outcomes.