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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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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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Stabilization of Beams with Nonlinear Feedback
SIAM Journal on Control and Optimization, 2002The author studies a simplified form of the dynamic Euler-Bernoulli beam equation for coupled beams: \(y''+\partial^4y/\partial x=0\), where \(y''\) stands for \(\partial^2y/\partial t^2\), \(t>0\), \(x\in(0,a)\cup (a,1)\), with a coupling point at \(x=a\). It is simply supported at \(x=0\), with shear hinge condition at \(x=1\) in model \(\#1\), it is
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Exchange of stabilities, symmetry, and nonlinear stability
Archive for Rational Mechanics and Analysis, 1985The paper, motivated in large part by the stability in a convection-like problem involving the gravity dependent motion of a suspension of swimming micro-organisms, is aimed to investigate the connection between the symmetric part of a linear operator and stability boundaries determined by the methods of linear theory and of nonlinear energy theory. It
Galdi, Giovanni P., Straughan, Brian
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Stability of Nonlinear Computing Schemes
SIAM Journal on Numerical Analysis, 1969by deriving necessary and sufficient conditions for the stability of nonlinear computing schemes. In ? 1, we motivate the concept of stability to be used here and provide the basic definitions. In ? 2, we prove the main theorem on stability which relates stability to conditions on the Frechet derivatives of the operators. As corollaries of this theorem
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STABILIZATION OF NONLINEAR PARABOLIC EQUATIONS
IFAC Proceedings Volumes, 1983Abstract We are concerned with the possibility of constructing implementable feedback control laws to stabilize ů + Au = f(u), primarily through the boundary conditions. Semigroup methods are employed to reduce the semi- linear problem to a linear one, to show stabilizability of certain parabolic problems by feedback and, finally, to show for the one-
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A characterization of the nonlinearity of d-stability
Journal of Mathematical Economics, 1975Abstract A set of equilibrium prices in a multiple commodity market is stable regardless of the adjustment rates in each market if and only if the Jacobian of the system is D-stable. In this note we show that a stable matrix is D-stable if and only if a certain pair of simultaneous nonlinear equations does not have a common zero over the range of ...
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Local Stability and Stabilization of Nonlinear Systems
1990In this chapter we will discuss some aspects of local stability and feedback stabilization of nonlinear control systems.
Henk Nijmeijer, Arjan van der Schaft
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Nonlinear Input-output Stability and Stabilization
1997In this paper we focus on the input-output method of stability analysis for nonlinear systems. The fundamental ideas underlying this method were developed in the 1960’s by authors such as Zames and Sandberg (see [8], [17], [9], [18] and the references therein). Some notable additional insight was provided by Safonov [7] in 1980. In the last five years,
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