Results 181 to 190 of about 6,844 (227)

On parametric instability of singularly perturbed systems

Automation and Remote Control, 2013
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Anatoliy A. Martynyuk, A. S. Khoroshun
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Singularly Perturbed Systems

1984
In this chapter we turn our attention to some vector boundary value problems which may be regarded as vector analogs of the scalar problems. However, as the reader will see, our results for vector problems are very incomplete, especially in comparison with the scalar theory.
K. W. Chang, F. A. Howes
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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 continuous spectrum of singularly perturbed operators

Nonlinear Oscillations, 2006
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Suboptimization of Singularly Perturbed Control Systems

SIAM Journal on Control and Optimization, 1992
The singularly perturbed control system \(\dot z=f_ 1(z,y,u)\), \(z(0)=z_ 0\), \(\varepsilon\dot y=f_ 2(z,y,u)\), \(y(0)=y_ 0\), is studied and compared with the `reduced system' \(\dot z=f_ 1(z,\psi(z,u),u)\), \(z(0)=z_ 0\), where \(y=\psi(z,u)\) is the root of the static equation \(0=f_ 2(z,y,u)\). It is shown that the reduced system approximates the
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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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Showalter regularization of a singularly perturbed PDE

Applied Mathematics and Computation, 2004
This paper deals with the Showalter regularization method applied to an ill-posed elliptic problem. Convergence is proved and numerical examples are also proposed.
Arindama Singh, S. Sheela
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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 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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Analytic Regularity for a Singularly Perturbed Problem

SIAM Journal on Mathematical Analysis, 1999
Summary: A singularly perturbed equation of elliptic-elliptic type in two dimensions is considered. We assume analyticity of the input data, i.e., the boundary of the domain is an analytic curve, the boundary data are analytic, and the right-hand side is analytic.
Melenk, Jens Markus, Schwab, Christoph
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