An exponential stabilization criterion for switched delayed interval type-2 fuzzy systems under admissible edge-dependent average dwell time mechanism

Abstract

This paper addresses the exponential stabilization of the switched interval type-2 fuzzy (IT-2F) time-delay systems under admissible edge-dependent average dwell time (AEDADT) scheme with a non-fragile memory state feedback controller. The IT-2F model depicts uncertain nonlinear systems where the lower and upper membership functions characterize the uncertain parameters. Unlike the previous works that relied on average dwell time (ADT), this work employs the concepts of slow switching and fast switching based on the AEDADT property for both stable and unstable modes. The main reason behind the integration is that fast switching has a great feature in restricting the unstable subsystems. Furthermore, in most nonlinear systems, the feedback control rate is realized by memoryless state feedback control. However, a time lag occurs between system state and control response. Therefore, a non-fragile memory state feedback controller is chosen to ensure the globally uniformly exponential stability condition for proposed nonlinear systems through the linear matrix inequalities (LMI) approach. A mode-dependent average dwell time (MDADT) switching scheme is compared with the described switching rule and derived the superiority of obtained results. The results demonstrate that the AEDADT switching rule is more flexible and achieves tighter bounds than the MDADT property. Finally, numerical simulations and comparisons are provided to illustrate the capability of proposed theoretical results.