Passivity-based fractional order integral sliding mode control and ε-bound estimation for nonlinear singularly perturbed systems

The Mittag-Leffler (M-L) stability and ε-bound estimation problem of fractional order integral sliding mode control (SMC) for nonlinear singularly perturbed systems (SPSs) based on robust passivity are studied. First, an integral-type switching surface function is devised considering singular perturbation parameter (SPP), and SMC law is constructed to satisfy accessibility of the switching surface. Then, linear matrix inequalities independent of SPP is derived thereby obtaining the gain matrix, which enables closed-loop SPS to be M-L stable and robustly passive. In addition, the upper bound of SPP is estimated, so that the sliding mode dynamic system will be robustly passive and M-L stable. Finally, a simulation example demonstrates the feasibility and effectiveness of SMC strategy based on passivity.

1 INTRODUCTION

Singularly perturbed systems (SPSs) are dynamical systems with small parameters and are characterized by multiple time scales [1], [2]. Due to their widespread existence and the pathological numerical problems that SPSs are prone to bring attract the attention of researchers, many achievements have been made in the study of SPSs using control synthesis methods and strategies in recent years, please refer to [3], [4] and their references.