منابع مشابه
External Stability and Continuous Liapunov Functions
It is well known that external stability of nonlinear input systems can be investigated by means of a suitable extension of the Liapunov functions method. We prove that a complete characterization by means of continuous Liapunov functions is actually possible, provided that the de nition of external stability is appropriately strengthened.
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We consider the problem of characterizing those systems which admit (weak) Liapunov functions with nice analytic properties. Our investigation gives a rather complete picture of the situation for the one-dimensional case.
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Dynamical systems with several equilibria occur in various fields of science and engineering: electrical machines, chemical reactions, economics, biology, neural networks. As pointed out by many researchers, good results on qualitative behaviour of such systems may be obtained if a Liapunov function is available. Fortunately for almost all systems cited above the Liapunov function is associated...
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In this paper we address the problem of characterizing the in nitesimal properties of functions which are non-increasing along all the trajectories of a di erential inclusion. In particular, we extend the condition based on the proximal gradient to the case of semicontinuous functions and Lipschitz continuous di erential inclusions. Moreover, we show that the same criterion applies also in the ...
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where/ : U—>R is continuous on the open set UC.RXR, is frequentlystudied by means of a continuous function V: U—*R. I t is sometimes unnecessary to know the solutions explicitly. If for example V is independent of /, V(xo) = 0 for some #o, V(x)>0 for XT^X^ and if for each solution of (E), V(</)(t)) is a monotonically decreasing function of t for t^Oy then x0 is a stable critical point of (E...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1965
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1965-11309-x