Homogeneous output‐feedback control with disturbance‐observer for a class of nonlinear systems

Summary In this article, we propose a finite‐time output‐feedback control scheme for a class of nonlinear systems. The dynamic part of the controller consists of an extended order observer, which is based on the higher order sliding‐mode exact differentiator. With such an observer, the states of the system are exactly estimated in finite‐time; moreover, the additional state in the observer estimates exactly and in finite‐time Lipschitz disturbances in the system. Such an estimation is used by the static part of the controller to compensate the disturbances. The static part of the controller can be chosen from a class of homogeneous controllers. The whole control scheme allows to recover in finite‐time several useful properties of homogeneous systems despite the additional and uncertain nonlinear terms. The effect of the noise in the measurement is also studied.