Robust L2 Disturbance Attenuation for Quasi-One-Sided Lipschitz Nonlinear Systems via Sliding Mode Control

This paper is concerned with the problem of $H_{\infty}-$sliding mode control (SMC) for a class of quasi one-sided Lipschitz (QOSL) nonlinear systems affected by unmatched uncertainties. The aims is to consider the bounded L2 disturbance attenuation measure in the analysis of sliding mode dynamics, thus to ameliorate the performance of the SMC system. Sufficient synthesis condition for the sliding mode dynamics is formulated in terms of linear matrix inequalities (LMIs). Then, an appropriate control law is synthesized such that reachability of the switching manifold is ensured. At last, a simulation example is given to prove the feasibility of the proposed approach.