Prescribed Performance-Guaranteed Tracking Control: A Switched Positive System Perspective

Abstract

This letter presents a new prescribed performance-guaranteed control (PPC) for a class of linear systems based on positive system theory. Different from standard PPC structure, our attention focuses on the positivity of distance between constrained state and associated performance boundaries. The original constrained system is mapped to a switched positive system involved in distance. This novel framework mitigates the vulnerability/sensitivity of the controller, as it eliminates the necessity for high-gain mechanisms to generate sufficient control input against constraint violations. It develops the performance boundary to a great extent, where various predetermined performance behaviors could be achieved without auxiliary structure. Both theoretical analysis and numerical simulation clarify the effectiveness of the proposed approach.