Exponential stability of fractional-order asynchronous switched impulsive systems with time delay and mode-dependent parameter uncertainty

Abstract

Distinguished from asymptotic stability or Mittag–Leffler stability of fractional-order synchronous switched impulsive systems, the exponential stability, implying explicit and faster convergence rate, is investigated in this paper for the fractional-order asynchronous switched impulsive systems with time delay and mode-dependent parameter uncertainty, where the addressed impulsive functions depend on not only switching modes but also impulsive sequences. Some novel criteria are developed via fractional differential delayed inequalities and LMIs technique, as well as the methods of induction and Lyapunov function, which establish a connection between fractional order, impulsive interval, impulsive function, time delay and average dwell time. In addition, our results extend the ones of fractional-order synchronous switched impulsive systems, and fractional-order asynchronous switched impulsive systems without time delay, which include the exponential stability of integer-order asynchronous switched impulsive systems with time delay as a special case. Finally, four numerical examples are presented to testify the theoretical achievements.