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.