Abstract

Given an unforced nonlinear system and two nested closed and invariant sets ¿ ¿ O, we present reduction principles allowing one to extrapolate the properties of stability, attractivity, and asymptotic stability of ¿ from analogous properties of the system restricted to O. As a corollary to our reduction principles, we present a stability criterion for cascade-connected systems which generalizes well-known results in the literature. Using the reduction principles, in Part II of this paper we present a comprehensive theory for passivity-based stabilization of closed sets.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.