2003
DOI: 10.1137/s0363012902407119
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Abstract: Abstract. This paper focuses on the stability analysis of systems having a continuum of equilibria. Two notions that are of particular relevance to such systems are convergence and semistability. Convergence is the property whereby every solution converges to a limit point that may depend on the initial condition. Semistability is the additional requirement that all solutions converge to limit points that are Lyapunov stable. We give new Lyapunov-function-based results for convergence and semistability of nonl… Show more

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Cited by 124 publications
(138 citation statements)
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“…In Section IV, we develop new Lyapunov-based results for semistability that do not make assumptions of sign definiteness on the Lyapunov functions. Instead, our results extend the results of [7] to discontinuous systems and use the notion of nontangency between the discontinuous vector field and weakly invariant or weakly negatively invariant subsets of the level or sublevel sets of the Lyapunov function. It is important to note that our stability results are different from the results in the literature [8], [9] since the Lipschitz conditions in [8], [9] are not valid for the autonomous differential inclusions considered in the paper.…”
Section: Introductionmentioning
confidence: 56%
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“…In Section IV, we develop new Lyapunov-based results for semistability that do not make assumptions of sign definiteness on the Lyapunov functions. Instead, our results extend the results of [7] to discontinuous systems and use the notion of nontangency between the discontinuous vector field and weakly invariant or weakly negatively invariant subsets of the level or sublevel sets of the Lyapunov function. It is important to note that our stability results are different from the results in the literature [8], [9] since the Lipschitz conditions in [8], [9] are not valid for the autonomous differential inclusions considered in the paper.…”
Section: Introductionmentioning
confidence: 56%
“…The following two lemmas and proposition extend related results from [7], and are needed for the main result of this section. Finally, we show that Mx Nx.…”
Section: Semistability Theory For Differential Inclusionsmentioning
confidence: 62%
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