On phase deficit of homogeneous sliding mode control

The notion of the phase deficit recently proposed in the literature is determined for systems with homogeneous higher order sliding mode (HOSM) controllers. The previously formulated criterion based on the phase deficit gives necessary conditions of finite-time convergence. A few homogeneous control algorithms of orders from two to five are analyzed. It is shown that, when the phase deficit is positive, the system controlled by an HOSM algorithm is capable of producing finite time convergence. However, under some controller parameters, a homogeneous HOSM controller may produce asymptotic conversion or even nonvanishing oscillations. Necessary conditions for finite-time convergence, infinite-time convergence, and finite-frequency oscillations are obtained through the developed approach.

Automated summary

The concept of phase deficit for systems with homogeneous higher order sliding mode (HOSM) controllers is discussed in the literature. Necessary conditions for finite-time convergence are derived based on the phase deficit, and several homogeneous control algorithms of different orders are analyzed. It is found that a positive phase deficit indicates finite time convergence, but under certain controller parameters, asymptotic conversion or nonvanishing oscillations may occur. The necessary conditions for finite-time convergence, infinite-time convergence, and finite-frequency oscillations are obtained through the developed approach.