Abstract
Input-to-state stability (ISS) and input–output L2-gain are two important robust stability concepts in analyzing the interconnections of nonlinear dynamical systems. In this paper, we demonstrate several qualitative equivalences between different ISS related properties and lp-gain properties for discrete-time systems via nonlinear changes of coordinates. Prior to that, certain summation-to-summation estimates are shown to be equivalent to the standard definitions of ISS and integral ISS (iISS) which lead to sufficient Lyapunov function conditions to verify lp-gain properties. Combined with known results on the equivalence of 0-input global asymptotic stability and iISS, and a superposition principle, we subsequently outline interesting implicative relationships between various discrete-time robust stability properties.
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 callDisclaimer: 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.
