Abstract
This paper proposes a Lyapunov approach to frequency analysis for general systems. The notion of frequency response is extended to general systems through a connection in linear systems. Lyapunov approaches to the characterization of frequency response are established for linear systems, homogeneous systems and nonlinear systems, respectively. In particular, we show that for linear systems, quadratic Lyapunov functions are sufficient for the characterization; for homogeneous systems, homogeneous Lyapunov functions are sufficient; and for general nonlinear systems, locally Lipschitz Lyapunov functions will be used. We also develop a Lyapunov approach for the characterization of the peak of the output. This approach is demonstrated to be effective on linear systems. An LMI based method for performing frequency analysis on linear differential inclusions is developed. Through a numerical example, an interesting phenomenon is observed about the relation between the frequency response and the L/sub 2/ gain of linear differential inclusions.
Published Version
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.
