摘要
This paper studies asymptotic stability of a continuous implementation of variablestructure control in which a signum function is approximated by a saturation nonlinearfunction. It is shown that the closed ring system is globally uniformly ultimately boundedwith respect to a compact set around the origin. This set can be made arbitrarily small byincreasing the gradient of the saturation function. Moreover, under slight additional suppositions, it is shown that in the absence of persistens disturbance the system has an uniformly asymptotically stable equilibrium point at the origin.
This paper studies asymptotic stability of a continuous implementation of variablestructure control in which a signum function is approximated by a saturation nonlinearfunction. It is shown that the closed ring system is globally uniformly ultimately boundedwith respect to a compact set around the origin. This set can be made arbitrarily small byincreasing the gradient of the saturation function. Moreover, under slight additional suppositions, it is shown that in the absence of persistens disturbance the system has an uniformly asymptotically stable equilibrium point at the origin.
