Results 171 to 180 of about 91,926 (215)

Singularly continuous spectrum of singularly perturbed operators

Nonlinear Oscillations, 2006
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Discrete Approximations of Singularly Perturbed Systems

2007
In the paper we study discrete approximations of singularly perturbed system in a finite dimensional space. When the right-hand side is almost upper semicontinuous with convex compact values and one-sided Lipschitz we show that the distance between the solution set of the original and the solution set of the discrete system is O(h1/2.
Tzanko Donchev, Vasile Lupulescu
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Scale-invariance in singularly perturbed systems

53rd IEEE Conference on Decision and Control, 2014
The property termed scale-invariance, or fold-change detection, represents a phenomenon that is observed in a variety of biological systems, ranging from bacterial to eukaryotic signaling pathways. Mathematically, it represents invariance of the complete output trajectory with respect to a rescaling of input magnitudes.
Maja Skataric, Evgeni V. Nikolaev, Eduardo D. Sontag   +2 more
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Singularly Perturbed Systems of Volterra Equations

Journal of Applied Analysis, 2002
This paper studies the behaviour of the solution \(u(t,\varepsilon)\) of the system of Volterra integral equations \[ \varepsilon u(t) = f(t) + \int_0^t A(t,s)u(s)\,ds, \quad 0 \leq t \leq T, \] as the positive parameter \(\epsilon\) tends to zero. Both \(f\) and \(A\) are continuous, and the eigenvalues of \(A(t,t)\) are supposed to be negative.
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On Invariant Manifolds in Singularly Perturbed Systems

Journal of Dynamical and Control Systems, 1999
The author deals with a slow-fast system \[ \dot x=f(x,y, \varepsilon), \quad \dot y=\varepsilon g(x,y, \varepsilon), \quad \dot\varepsilon=0 \] where \(x\in\mathbb{R}^\ell\), \(y\in\mathbb{R}^m\), \(\varepsilon\in \mathbb{R}\). Assuming that the fast system \(\dot x=f(x,y,0)\), \(\dot y=0\) has a compact smooth invariant manifold with boundary \(M_0 ...
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On hopf bifurcations in singularly perturbed systems

IEEE Transactions on Automatic Control, 2003
It has been shown recently that, under some generic assumptions, there exists a Hopf curve /spl lambda/ = /spl lambda/ (/spl epsiv/) for singularly perturbed systems of the form x/spl dot/ = f (x, y, /spl lambda/), /spl epsiv/y/spl dot/ = g(x, y, /spl lambda/) near the singular surface defined by det g/sub v/ = 0.
L. Yang, Yun Tang, Dongyun Du
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Singularly Perturbed Optimal Tracking Problem

Differential Equations
We consider a singularly perturbed optimal tracking problem with a given etalon trajectory in the case of incomplete information about the state vector in the presence of external disturbances. To analyze the differential equations that arise when solving this problem, the decomposition method is used, which is based on the technique of integral ...
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Relaxation in singularly perturbed control systems

Proceedings of the 41st IEEE Conference on Decision and Control, 2002., 2004
When slow and fast motions are coupled in a singularly perturbed control system, the application of relaxed controls may be needed on several levels. There may be a need to relax the control affecting the slow and the fast motions and there may be a need to relax the fast flow itself, which serves as a control for the slowly dynamics.
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Dissipativity of Singularly Perturbed Lur’e Systems

IEEE Transactions on Circuits and Systems II: Express Briefs, 2019
The problem of singularly perturbed Lur’e systems is investigated in this brief. Two new storage functions are constructed to explore the dynamics of both the fast and slow models, as well as their interaction more efficiently. By using the merit of the proposed storage functions, some new $\varepsilon $ -uniformly strict dissipativity criteria in
Yan-Wu Wang, Wu Yang 0003, Xiao-Kang Liu 0001, Wu-Hua Chen   +3 more
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Singularly Perturbed Operators

1994
Let A = A* > 1 be a self-adjoint unbounded operator in a separable complex Hilbert space H.
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