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Investigation of Exponential Dichotomy of Itô Stochastic Systems by Using Quadratic Forms
Ukrainian Mathematical Journal, 2001The author studies the stochastic Itô system \[ dx=A(t)x dt+\sum_{i=1}^{m}B_i(t)x dW_i(t).\tag{1} \] Here, \(A(t),B_1(t),\ldots,B_m(t)\) are deterministic matrices defined on the semi-axis \(t\geq 0\) and \(W_1(t),\ldots W_m(t)\) are totally independent scalar Wiener processes determined on a complete probability space \((\Omega,F,\text{P})\).
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Quadratic normal forms of nonlinear control systems with uncontrollable linearization
Proceedings of 1995 34th IEEE Conference on Decision and Control, 2002The controller normal form of linear systems has been a useful tool for the study of many linear control problems. In Wei Kang and Krener (1992), Wei Kang (1991,1994), and Krener and Wei Kang (1991), normal forms of nonlinear control systems are found for linearly controllable systems. In this paper, the author addresses the problem of quadratic normal
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Deformations of Diophantine Systems for Quadratic Forms of the Root Lattices A n
Journal of Mathematical Sciences, 2006The matrix equation \(Q[X] = {^tT}QT = A\) is studied, where \(Q\) and \(A\) are positive definite symmetric integral matrices of order \(n\) and \(m\), respectively, and \(T\) ranges over the set of \(n\times m\) integer matrices. When \(A = A' \oplus A''\), where the summands have squarefree and coprime determinants, a formula is found for the ...
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Representation of integers by a system of additive, positive quadratic forms
Journal of Soviet Mathematics, 1979By the circle method, an asymptotic formula is obtained for the number of solutions of the system of equations $$\sum\limits_{j = 1}^s {q_{jk} x_j^2 = n_k } \left( {k = 1, \ldots ,2} \right)$$ , where qjk are given positive integers and nk are increasing ...
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Communications in Nonlinear Science and Numerical Simulation, 2015
Manuel A Duarte-Mermoud +2 more
exaly
Manuel A Duarte-Mermoud +2 more
exaly
Quadratic forms in normal RVs: theory and applications to OSTBC over hoyt fading channels
IEEE Transactions on Wireless Communications, 2008Athanasios Rontogiannis +2 more
exaly
On Quadratic Bent Functions in Polynomial Forms
IEEE Transactions on Information Theory, 2007Honggang Hu
exaly
The explicit linear quadratic regulator for constrained systems
Automatica, 2002Alberto Bemporad +2 more
exaly

