This article delves into the relative order and feedback characteristics of nonlinear counterclockwise input-output (CCW I-O) systems. Firstly, based on the theory of dissipation and the Lie algebra method, this paper provides sufficient conditions for the nonlinear CCW I-O system to have relative orders 2 at the origin, and proves that the strict CCW I-O system has the minimum phase characteristic. Secondly, this article delves into the necessary and sufficient conditions for nonlinear systems to possess feedback CCW I-O characteristics, which require the system to have a relative order 2 at the origin and be a weakly minimum phase system. These achievements not only expand the application scope of CCW I-O theory, especially for systems with relative order 2, but also provide effective analysis tools and design methods for systems with such characteristics in engineering fields such as flexible structures and nano-positioning. With the help of representative typical examples, the accuracy and practical application value of the theoretical results obtained are comprehensively verified. Future research will focus on relaxing matching conditions and exploring output feedback strategies.
