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Almost Sure Stability of Nonlinear Systems Under Random and Impulsive Sequential Attacks
IEEE Transactions on Automatic Control, 2020This article is concerned with the stability problem for a class of Lipschitz-type nonlinear systems in networked environments, which are suffered from random and impulsive deception attacks.
Wangli He +3 more
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Differential Stability in Nonlinear Programming
SIAM Journal on Control and Optimization, 1977This paper consists of a study of stability and differential stability in nonconvex programming. For a program with equality and inequality constraints, upper and lower bounds are estimated for the potential directional derivatives of the perturbation function (or the extremal-value function).
Gauvin, Jacques, Tolle, Jon W.
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Stochastic Stability of Nonlinear Oscillators
SIAM Journal on Applied Mathematics, 1988The authors study the stability behavior of a non-linear oscillator parametrically excited by a stationary Markov process. They modify the notion of stability by considering \(H(E_ 0)=\sup_{t>0}E(t,E_ 0)\), where \(E(t)=U(x(t))+\dot x(t)^ 2\) is the sum of potential and kinetic energy, rather than the usual \(\sup_{t>0}| \vec x(t,\vec x_ 0)|\), where \(
Kłosek-Dygas, M. M. +2 more
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Nonlinear stability for Eady’s model
Applied Mathematics and Mechanics, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liu, Yong-Ming, Qiu, Ling-Cun
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The Physics of Fluids, 1976
The nonlinear energy theorem of Rosenbluth for helically symmetric tokamak magnetohydrodynamic motions is used to find nonlinear corrections to the linear stability of kink modes. Near marginal stability these corrections are important and give a finite amplitude threshold for instability. Cases are also found in which a mode saturates at low amplitude,
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The nonlinear energy theorem of Rosenbluth for helically symmetric tokamak magnetohydrodynamic motions is used to find nonlinear corrections to the linear stability of kink modes. Near marginal stability these corrections are important and give a finite amplitude threshold for instability. Cases are also found in which a mode saturates at low amplitude,
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Bifurcation in Nonlinear Hydrodynamic Stability
SIAM Review, 1975The appearance of secondary motions in a viscous fluid field can be understood to some extent as a bifurcation phenomenon with exchange of stability between the basic and the secondary flow. This article summarizes the main mathematical results of bifurcation and stability in hydrodynamic stability theory so far obtained.
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EXTERNAL STABILITY OF NONLINEAR SYSTEMS
IFAC Proceedings Volumes, 1995Abstract The aim of this note is to present and characterize a notion of external stability for nonlinear systems. Moreover, relationship with appropriate internal stability properties are discussed. Finally, we give a partial answer to the problem of external stabilizability by means of feedback.
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Selectivity and Stability via Dendritic Nonlinearity
Neural Computation, 2007Inspired by recent studies regarding dendritic computation, we constructed a recurrent neural network model incorporating dendritic lateral inhibition. Our model consists of an input layer and a neuron layer that includes excitatory cells and an inhibitory cell; this inhibitory cell is activated by the pooled activities of all the excitatory cells ...
Morita, Kenji +2 more
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Exponential Stability of Nonlinear Systems With Delayed Impulses and Applications
IEEE Transactions on Automatic Control, 2019We consider a class of nonlinear impulsive systems with delayed impulses, where the time delays in impulses exist between two consecutive impulse instants. Based on the impulsive control theory and the ideas of average dwell time (ADT), a set of Lyapunov-
Xiaodi Li, Shiji Song, Jianhong Wu
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