Passivity-Based Integral Sliding Mode Control and $\varepsilon$ - Bound Estimation for Uncertain Singularly Perturbed Systems With Disturbances

This brief addresses the problems of passivity-based integral sliding mode control (ISMC) and ε-bound estimation for uncertain singularly perturbed systems (SPSs) with disturbances. First, a singular perturbation parameter ε-dependent integral sliding surface is constructed with the reachability condition satisfied. Then, by passivity theory, a set of ε-independent linear matrix inequalities are derived to design the ISMC gain, such that the closed-loop SPSs are passive and internally exponentially stable. Furthermore, an ε-bound estimation method is proposed, such that the passivity and internally exponential stability are preserved for any ε less than or equal to the ε-bound. Compared with the existing methods, the proposed approaches are less conservative because they are derived by a more general storage function and are free of equality constraints. Finally, the advantages and effectiveness of the proposed methods are demonstrated by simulation results.