A new approach to stabilization of high‐order nonlinear systems with an asymmetric output constraint

Abstract

SummaryThis paper is concerned with the problem of state feedback stabilization for a class of high‐order nonlinear systems with an asymmetric output constraint. A novel asymmetric barrier Lyapunov function (BLF) is first proposed by deliberating the characteristics of the system nonlinearities. Then, the presented BLF, together with a skillful manipulation of sign functions, is utilized to delicately revamp the technique of adding a power integrator, thereby developing a systematic approach that guides us in constructing a continuous state feedback stabilizer and preventing the violation of a pre‐specified asymmetric output constraint during operation. The novelty of this paper is attributed to the development of a unified method that is able to simultaneously tackle the problem of stabilization for high‐order nonlinear systems with and without output constraints in a constructive fashion, without changing the controller structure. An illustrative example is presented to demonstrate the superiority of the proposed approach.