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Global Asymptotic Stability and Stabilization of Neural Networks With General Noise
IEEE Transactions on Neural Networks and Learning Systems, 2018Neural networks (NNs) in the stochastic environment were widely modeled as stochastic differential equations, which were driven by white noise, such as Brown or Wiener process in the existing papers. However, they are not necessarily the best models to describe dynamic characters of NNs disturbed by nonwhite noise in some specific situations.
Qihe Shan +3 more
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Global Asymptotic Stability of a Generalized Liénard Equation
SIAM Journal on Applied Mathematics, 1970is necessary and sufficient for the global asymptotic stability of the equilibrium point (0, 0) of (1.2). The idea of the proof is to show that (1.3) is necessary and sufficient for the boundedness of all solutions of (1.2). In doing this the crucial step is determining whether a solution with initial conditions in the first quadrant (third quadrant ...
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Global asymptotic stability and symmetric periodic solutions
Journal of the Franklin Institute, 1972Abstract The global asymptotic stability of “second-order” relay control systems with negative eigenvalues is shown to be a consequence of the nonexistence of symmetric periodic solutions. The result shows further that, except for a special case, the solutions reach the origin in finite time.
Eisenfeld, J., Sadler, J. P.
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Global asymptotic stability of non-linear difference equations II
Economics Letters, 1986zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Global -exponential asymptotic stabilization of underactuated surface vessels
Systems & Control Letters, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Global asymptotic stability of non-linear difference
Economics Letters, 1990Abstract A sufficient condition for global asymptotic stability of the origin for non-linear difference equations is presented without assuming the differentiability of the iteration function. This conditions is a generalization of the results of Okuguchi (1977), Fujimoto (1987), and Wu and Brown (1989).
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Global asymptotic stability for nonlinear difference equations
Applied Mathematics and Computation, 2006Consider the nonlinear difference equation \[ x_{n+1}-x_{n}+a_{n}x_{n-k}=b_{n}f(x_{n-l})~\;\;\;,~\;\;n\geq 0,\tag{\(*\)} \] where \(l,~k\) are nonnegative integers, \(\{a_{n}\}\) \ and \ \(\{b_{n}\}\) \(\;\)\ are two sequences of real numbers, and \(a_{n}\geq 0\) for \ \(n=0,1,2,\dots,f\in C((-\infty ,\infty )~,~(-\infty ,\infty )).\) The author ...
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Global Asymptotical Stability of Internet Congestion Control
2007A class of Internet congestion control algorithms with communication delays is studied. The algorithm is a pieced continuous function that will be switched on the rate of the source. Based on the Lyapunov theorem, the Lyapunov stability of the system is analyzed.
Hong-yong Yang +3 more
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GLOBAL ASYMPTOTIC STABILITY AND GLOBAL EXPONENTIAL STABILITY OF HOPFIELD NEURAL NETWORKS
Wavelet Analysis and Its Applications, and Active Media Technology, 2004SHOU-MING ZHONG +3 more
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