Weighted homogeneity and robustness of sliding mode control

General features of finite-time-stable (FTS) homogeneous differential inclusions (DIs) are investigated in the context of sliding-mode control (SMC). The continuity features of the settling-time functions of FTS homogeneous DIs are considered, and the system asymptotic accuracy is calculated in the presence of disturbances, noises and delays. Performance of output-feedback multi-input multi-output homogeneous SMC systems is studied in the presence of relative degree fluctuations. The bifurcation of the kinematic-car-model relative degree is analyzed as an example.