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Linear systems with quadratic outputs
2017 American Control Conference (ACC), 2017We study linear systems with quadratic outputs. Our goal is to analyze and control the evolution of such quadratic outputs under a given linear control system. In this spirit, we first attempt to find a differential equation governing the evolution of the outputs in order to consequently be able to control this evolution.
Jan Maximilian Montenbruck +2 more
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On the stabilization of quadratic nonlinear systems
European Journal of Control, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Oumoun, Mohamed +2 more
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Stability Analysis of Quadratic Systems
IFAC Proceedings Volumes, 1989A n-order quadratic system is considered and an analysis of the domain of attraction of its origin is developed in the paper. The presented method selects a quadratic Lyapunov function V on the basis of the linear part of the system under study and of possible information about the field where such a system holds.
R. Genesio, A. Tesi
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Geometry of cycles in quadratic systems
Qualitative Theory of Dynamical Systems, 2002The paper is devoted to study of the affine and Euclidean differential geometric properties of cycles occurring in the phase plane of a quadratic system of differential equations. It is shown that every quadratic cycle has exactly six affine vertices and the number of Euclidean vertices can vary, not just from cycle to cycle, but for the same cycle ...
Shafer, Douglas S., Zegeling, André
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QUADRATIC PERTURBATIONS OF A CLASS OF QUADRATIC REVERSIBLE LOTKA–VOLTERRA SYSTEMS
International Journal of Bifurcation and Chaos, 2013This paper is concerned with the bifurcation of limit cycles of a class of quadratic reversible Lotka–Volterra system [Formula: see text] with b = -1/3. By using the Chebyshev criterion to study the number of zeros of Abelian integrals, we prove that this system has at most two limit cycles produced from the period annulus around the center under ...
Yi Shao, A. Chunxiang
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Error Bounds for Quadratic Systems
2000In this paper we consider the problem of estimating the distance from a given point to the solution set of a quadratic inequality system. We show, among other things, that a local error bound of order 1/2 holds for a system defined by linear inequalities and a single (nonconvex) quadratic equality.
Luo, Z-Q, Sturm, J.F.
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A RIKITAKE TYPE SYSTEM WITH QUADRATIC CONTROL
International Journal of Bifurcation and Chaos, 2012A Rikitake type system with quadratic control having a negative tuning parameter is considered and some of the geometrical and dynamical properties are analyzed.
Cristian Lazureanu, Tudor Bînzar
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Deformations of quadratic Diophantine systems
Izvestiya: Mathematics, 2001Consider the matrix equation \(Q[X] = {^tX}QX = A\), where \(Q\) and \(A\) are positive definite symmetric integral matrices of order \(n\) and \(m\), respectively, and \(X\) ranges over the set of \(n\times m\) integer matrices. The author studies the relationship between solutions to this equation and corresponding equations \(K'[Y]=A''\) obtained by
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Proceedings., 33rd Annual Symposium on Foundations of Computer Science, 1992
The paper promotes the study of computational aspects, primarily the convergence rate, of nonlinear dynamical systems from a combinatorial perspective. The authors identify the class of symmetric quadratic systems. Such systems have been widely used to model phenomena in the natural sciences, and also provide an appropriate framework for the study of ...
Y. Rabinovich, A. Sinclair, A. Wigderson
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The paper promotes the study of computational aspects, primarily the convergence rate, of nonlinear dynamical systems from a combinatorial perspective. The authors identify the class of symmetric quadratic systems. Such systems have been widely used to model phenomena in the natural sciences, and also provide an appropriate framework for the study of ...
Y. Rabinovich, A. Sinclair, A. Wigderson
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OSCILLATIONS AND CHAOS IN SIMPLE QUADRATIC SYSTEMS
International Journal of Bifurcation and Chaos, 2008This paper is concerned with the study of third order quadratic and autonomous systems and the interest is oriented to the stable periodic oscillations. From the "jerk" equation model, the classes of minimal complexity presenting a Hopf bifurcation are derived and their local characterization is carried out by means of a suitable harmonic balance ...
INNOCENTI, GIACOMO +2 more
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