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Phase portraits of Bernoulli quadratic polynomial differential systems
Electronic Journal of Differential Equations, 2020 In this article we study a new class of quadratic polynomial differential systems. We classify all global phase portraits in the Poincare disk of Bernoulli quadratic polynomial differential systems in R^2.
Jaume Llibre +2 more
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On point-dissipative systems of differential equations with quadratic nonlinearity [PDF]
International Journal of Mathematics and Mathematical Sciences, 1991 The system x′=Ax+f(x) of nonlinear vector differential equations, where the nonlinear term f(x) is quadratic with orthogonality property xTf(x)=0 for all x, is point-dissipative if ...
Anile K. Bose +2 more
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Synthesis of dissipative systems using quadratic differential forms: Part I [PDF]
IEEE Transactions on Automatic Control, 2002 In this second part of this paper, we discuss several important special cases of the problem solved in Part I. These are: disturbance attenuation and passivation, the full information case, the filtering problem, and the case that the to-be-controlled plant is given in input–state–output representation.
H L Trentelman, J C Willems
exaly +6 more sources
UNCERTAIN SYSTEMS, BEHAVIOURS AND QUADRATIC DIFFERENTIAL FORMS [PDF]
IFAC Postprint Volumes IPPV / International Federation of Automatic Control, 2002 Abstract This paper considers uncertain systems from a behavioural point of view defined via quadratic differential forms. This uncertainty definition is closely related to the integral quadratic constraint uncertainty description commonly found in robust control theory.
Ian Petersen, Jan Camiel Willems
exaly +2 more sources
Abel quadratic differential systems of second kind
Electronic Journal of Differential EquationsThe Abel differential equations of second kind, named after Niels Henrik Abel, are a class of ordinary differential equations studied by many authors. Here we consider the Abel quadratic polynomial differential equations of second kind denoting this class by \(QS_{Ab}\).
Joan C. Artes +3 more
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Liouvillian first integrals of quadratic–linear polynomial differential systems
Journal of Mathematical Analysis and Applications, 2011 For a large class of quadratic-linear polynomial differential systems with a unique singular point at the origin having non-zero eigenvalues, we classify the ones which have a Liouvillian first integral, and we provide the explicit expression of them.
Claudia Valls, Jaume Llibre
exaly +3 more sources
Bifurcations of the Riccati Quadratic Polynomial Differential Systems [PDF]
International Journal of Bifurcation and Chaos, 2021 In this paper, we characterize the global phase portrait of the Riccati quadratic polynomial differential system [Formula: see text] with [Formula: see text], [Formula: see text] nonzero (otherwise the system is a Bernoulli differential system), [Formula: see text] (otherwise the system is a Liénard differential system), [Formula: see text] a ...
Jaume Llibre +2 more
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On limit cycles of piecewise differential systems formed by arbitrary linear systems and a class of quadratic systems [PDF]
Mathematica Bohemica, 2023 We study the continuous and discontinuous planar piecewise differential systems separated by a straight line and formed by an arbitrary linear system and a class of quadratic center.
Aziza Berbache
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Adaptive Control of Differentially Private Linear Quadratic Systems [PDF]
2021 IEEE International Symposium on Information Theory (ISIT), 2021 In this paper, we study the problem of regret minimization in reinforcement learning (RL) under differential privacy constraints. This work is motivated by the wide range of RL applications for providing personalized service, where privacy concerns are becoming paramount.
Sayak Ray Chowdhury +2 more
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Fundamental response in the vibration control of buildings subject to seismic excitation with ATMD
Selecciones Matemáticas, 2023 The linear quadratic regulator for vibration systems subject to seismic excitations is discussed in his own physical newtonian space as a second-order linear differential system with matrix coefficients.
Fidel Jara Huanca +2 more
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