Minimum phase Properties Based on High-Gain Output Feedback Stability Analysis

Abstract

Abstract In this paper, a new definition of the minimum phase property based on high gain output feedback stability (HGS) is introduced. The minimum phase systems with respect to this definition have stable inverses leading to no performance limitations. In other words, the minimum norm of regulation or tracking error for these systems approaches zero. This set of minimum phase linear systems includes systems with stable zeros (i.e., the zeros with negative real parts and/or simple imaginary zeros); however, the usual definition of minimum phase systems considers only systems with zeros located in the open left half plane (LHP). The difficulty of minimum phase determination in nonlinear systems highlights better the main objective of the paper to look for a way to modify the minimum phase concept in some extent to obtain more feasible conditions, which can be applied to a larger class of systems. It should be noted that based on this new definition, the minimum phase determination can be easily checked out through stability analysis of the closed loop system. Furthermore, knowing the fact that both performance limitation and stable inverse criteria can be potentially extended to nonlinear systems, this paper employs these concepts to reflect better the strength of the proposed minimum phase property. Finally, we apply the proposed method to two nonlinear systems. The simulation results easily approve the effectiveness of the method developed fully in the paper.