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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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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The standard conjugate gradient (CG) method uses orthogonality of the residues to simplify the formulas for the parameters necessary for convergence. In adaptive filtering, the sample-by-sample update of the correlation matrix and the cross-correlation vector causes a loss of the residue orthogonality in a modified online algorithm, which, in turn, results in loss of convergence and an increase...
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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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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1978
ISSN: 0022-247X
DOI: 10.1016/0022-247x(78)90235-4