Robust output‐feedback finite‐time regulator of systems with mismatched uncertainties bounded by positive functions

In this study, the authors investigate the problem of finite‐time output regulation for a class of mismatched uncertain n ‐dimensional integrator, in which only the output signal is measurable and the higher derivatives of the matched and mismatched disturbances are bounded by time‐varying functions. Based on a finite‐time extended state observer, an output feedback controller is constructed. It is shown that even in the presence of mismatched uncertainties, whose high‐order derivatives are bounded by positive functions, the output of the system can be regulated to zero in finite time without requiring the knowledge of full‐state signals. An application to mass‐spring mechanical systems is given to illustrate the effectiveness and attractive properties of the authors' proposed controller.