LaSalle–Yoshizawa Theorem for nonlinear systems with external inputs: A counter-example

Title: LaSalle–Yoshizawa Theorem for nonlinear systems with external inputs: A counter-example
Creator: Chen, Zhiyong
Relation: Automatica Vol. 147, no. 110636
Publisher Link: http://dx.doi.org/10.1016/j.automatica.2022.110636
Publisher: Elsevier
Resource Type: journal article
Date: 2023
Description: LaSalle–Yoshizawa Theorem is an important tool in guaranteeing convergence of a nonlinear time-varying adaptive system. It claims boundedness and convergence when the derivative of a Lyapunov function is negative semidefinite. For a nonlinear system with an external input, the input-to-state stability (ISS) Lyapunov theorem reveals boundedness of system solutions when the derivative of an ISS Lyapunov function is negative definite with an input term. It is interesting to seek a LaSalle–Yoshizawa like criterion for a nonlinear system with an external input. An intuitive question is whether a certain boundedness property is guaranteed when the derivative of an ISS Lyapunov function is negative semidefinite with an input term. This technical communique gives a negative answer with a counter-example.
Subject: nonlinear systems; Lyapunov stability theorem; LaSalle-Yoshizawa theorem; input-to-state stability
Identifier: http://hdl.handle.net/1959.13/1489313
Identifier: uon:52678
Identifier: ISSN:0005-1098
Language: eng
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