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APPLICATIONS OF SYSTEMS OF QUADRATIC FORMS TO GENERALISED QUADRATIC FORMS
Bulletin of the Australian Mathematical Society, 2020A system of quadratic forms is associated to every generalised quadratic form over a division algebra with involution of the first kind in characteristic two. It is shown that this system determines the isotropy behaviour and the isometry class of generalised quadratic forms.
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The Quadratic Criterion for Distributed Systems
SIAM Journal on Control, 1969Abstract : The article explores the applicability of the quadratic criterion of optimality to the control of distributed parameter systems or, alternatively, to differential equations in a Hilbert space. It is shown that such application is indeed possible and, perhaps more important from the engineering point of view, that the optimal controls thus ...
Lukes, D. L., Russell, D. L.
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Mathematics of Control, Signals, and Systems, 1991
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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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Quadratic stabilization of switched systems
International Journal of Systems Science, 2005We consider quadratic stabilization of uncertain switched systems when a switching rule is imposed on state feedback controllers of subsystems. A method is proposed to constructively design switching rules for continuous and discrete-time switched systems with norm-bounded time-varying uncertainties.
Zhijian Ji +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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