Semiglobal finite-time stabilization via output-feedback for a class of high-order uncertain nonlinear systems

This paper is devoted to the semiglobal finite-time stabilization via output-feedback for a class of high-order uncertain nonlinear systems. This problem can hardly be solved by the existing schemes, mainly since the systems under investigation contain unknown control coefficients which are dominated by the known functions of system states, and possess more serious nonlinearities which allow arbitrary-high-order growing unmeasurable states. However, for the global case, the system unknown control coefficients should be dominated by the known functions of output and the system nonlinearities merely allow homogeneous-order growing unmeasurable states, and therefore our semiglobal objective significantly weakens the restrictions on the control coefficients and the nonlinearities of the systems. In this paper, with the assumption that all the system states are available for feedback, a state-feedback controller is first constructed by adding a power integrator, which ensures that the closed-loop system is globally finite-time stable. Then, by certainty equivalence principle and saturation technique, an output-feedback controller is successfully constructed, which makes the closed-loop system semiglobal attractive and local finite-time stable. A simulation example is presented to illustrate the effectiveness of the proposed method.