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STABILIZATION OF PLANAR NONLINEAR SYSTEMS
IFAC Proceedings Volumes, 1992Abstract In this paper, we investigate the C1-stabilizability of affine control nonlinear systems in the plane. The feedback laws are given by means of Center manifold machinery.
R. Chabour, A. Iggidr
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Nonlinear stabilization with bounded controller
2015 10th Asian Control Conference (ASCC), 2015This In this paper, an extension of the Sontag's universal formula is proposed. For benchmark, the proposed method is compared with two other approaches, i.e. a universal Sontag's formula and a direct Lyapunov with comparing square. To observe the efficacy of the proposed method, a numerical nonlinear system with cubic damping is stabilized.
Muhammad Nizam Kamarudin +3 more
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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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Stability of nonlinear asynchronous systems
2007 46th IEEE Conference on Decision and Control, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
David Muñoz de la Peña +1 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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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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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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Nonlinear Stability of a Liquid Jet
The Physics of Fluids, 1970A nonlinear analysis is presented for the capillary stability of a cylindrical column of liquid, of circular cross section. A second-order expansion is obtained using the method of multiple time scales. It is found that the cutoff wavenumber which separates stable from unstable disturbances is amplitude dependent, in agreement with Yuen, and contrary ...
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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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