Finite-time stabilization via output feedback for high-order planar systems subjected to an asymmetric output constraint

Abstract

This article addresses the problem of finite-time stabilization via output feedback for high-order planar systems subjected to an asymmetric output constraint. By delicately exploring the features of nonlinearities and utilizing skillful manipulations of signum functions, a new fraction-type asymmetric barrier Lyapunov function and a distinctive non-smooth state observer are developed. On the basis of the proposed barrier Lyapunov function along with the state observer, the celebrated adding a power integrator technique is elegantly renovated to develop a novel approach by which a continuous output feedback finite-time stabilizer is constructed in a systematic fashion while ensuring the fulfillment of a pre-specified asymmetric output constraint. The presented scheme is a unification approach able to achieve the finite-time stabilization via output feedback for systems subjected to or free from output constraints simultaneously, without needing to change both the controller and observer structures. A numerical is provided to illustrate the superiority of the developed method.