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On quadratic differential forms for n-D systems
Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187), 2002A study of quadratic differential forms for 1-D systems was carried out in Willems and Trentelman (1998). Extention and study of this concept of quadratic differential forms to n-D systems is the main purpose of the paper. This extension opens the way to generalization of several concepts of 1-D systems, like that of conservative systems and ...
Harish K. Pillai, Etar Rogers
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The Floquet Solution for Systems with Quadratic Form Hamiltonians
Physica Scripta, 1999Summary: We consider the class of Hamiltonians composed of a quadratic form in the canonical operators and a linear interaction term with time periodic external fields of an arbitrary strength. The Hamiltonian can be made time independent by a unitary transformation in the extended Hilbert space, which has the meaning of a time-dependent translation in
Lungu, Radu Paul, Manolescu, Andrei
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Systems of rational quadratic forms
Archiv der Mathematik, 2004Let \(Q_1,\dots, Q_r\in\mathbb{Q}[X_1,\dots, X_s]\) be quadratic forms. It was shown by \textit{W. M. Schmidt} [Theorie des nombres, Semin. Delange-Pisot-Poitou, Paris 1980--81, Prog. Math. 22, 281--307 (1982; Zbl 0492.10017)] that the number of simultaneous integral solutions of size at most \(p\) is \(cP^{s-2r}+ o(P^{s-2r})\) providing that every ...
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Extended normal forms of quadratic systems
29th IEEE Conference on Decision and Control, 1990A set of extended quadratic controller normal forms of linearly controllable systems with single input is given. These normal forms are considered as the extension of the form due to P. Brunovsky (1970) to the nonlinear systems. It is proved that, given a nonlinear system, there exists a dynamic feedback so that the extended system has a linear ...
A.J. Krener, W. Kang
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Observability quadratic normal form for discrete-time systems
IEEE Transactions on Automatic Control, 2005This note deals with quadratic observability normal form for nonlinear discrete-time single-input-single-output (SISO) system. First of all, the main concept of quadratic equivalence with respect to the observability property, is introduced for discrete-time systems.
Iman Belmouhoub +2 more
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Quadratic form of stable sub‐manifold for power systems
International Journal of Robust and Nonlinear Control, 2004AbstractThe stable sub‐manifold of type‐1 unstable equilibrium point is fundamental in determining the region of attraction of a stable working point for power systems, because such sub‐manifolds form the boundary of the region (IEEE Trans. Automat. Control 1998; 33(1):16–27; IEEE Trans. Circuit Syst. 1988; 35(6):712–728).
Cheng, Daizhan +3 more
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On the zeta-functions of systems of quadratic forms
Mathematical Notes of the Academy of Sciences of the USSR, 1976We prove that the zeta-function of m variables of a system of m positive-definite quadratic forms has a meromorphic analytic continuation onto the whole m-dimensional complex space.
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Quadratic Forms on Complex Random Matrices and Multiple-Antenna Systems
IEEE Transactions on Information Theory, 2005In this correspondence, the densities of quadratic forms on complex random matrices and their joint eigenvalue densities are derived for applications to information theory. These densities are represented by complex hypergeometric functions of matrix arguments, which can be expressed in terms of complex zonal polynomials. The derived densities are used
Ratnarajah, Tharmalingam +1 more
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SIMULTANEOUS ZEROS OF A SYSTEM OF TWO QUADRATIC FORMS
2020In this dissertation we investigate the existence of a nontrivial solution to a system of two quadratic forms over local fields and global fields. We specifically study a system of two quadratic forms over an arbitrary number field. The questions that are of particular interest are: How many variables are necessary to guarantee a nontrivial zero to a ...
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Systems Of Quadratic Forms Over Local Fields.
1969PhD ; Mathematics ; University of Michigan, Horace H. Rackham School of Graduate Studies ; http://deepblue.lib.umich.edu/bitstream/2027.42/179958/2/7014638 ...
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