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Further results on Mittag-Leffler synchronization of fractional-order coupled neural networks
Advances in Difference Equations, 2021 In this paper, we focus on the synchronization of fractional-order coupled neural networks (FCNNs). First, by taking information on activation functions into account, we construct a convex Lur’e–Postnikov Lyapunov function.
Fengxian Wang, Fang Wang, Xinge Liu
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Nonexistence of Lyapunov exponents for matrix cocycles [PDF]
Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 2017 It follows from Oseledec Multiplicative Ergodic Theorem that the Lyapunov-irregular set of points for which the Oseledec averages of a given continuous cocycle diverge has zero measure with respect to any invariant probability measure. In strong contrast, for any dynamical system $f:X\rightarrow X$ with exponential specification property and a H$\ddot{\
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at - Automatisierungstechnik, 2019 A novel approach for the design of delayed output-feedback controllers that optimize a quadratic cost function is presented. The proposal is based on the formulation of the optimization of the quadratic performance criterion as a minimization problem ...
Marco A. Gómez, W. Michiels, S. Mondié
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Construction of Hierarchical Matrix Lyapunov Functions
Journal of Mathematical Analysis and Applications, 1994 Consider the differential system (*) \(dx/dt =f(t,x)\) having \(x=0\) as unique stationary solution. Assume that there exists a decomposition of (*) in the form \[ dx_1/dt =f_1(t, x_1) +h_1(t,x_1, x_2),\;dx_2/dt= f_2(t,x_2) +h_2(t,x_1,x_2). \tag{**} \] Furthermore, assume there exists a decomposition of the systems \(dx_k/dt= f_k(t,x_k)\), \(k=1,2 ...
Martynyuk, A.A. +2 more
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Lyapunov matrices approach to the parametric optimization of a neutral system
Archives of Control Sciences, 2016 In the paper a Lyapunov matrices approach to the parametric optimization problem of a neutral system with a P-controller is presented. The value of integral quadratic performance index of quality is equal to the value of Lyapunov functional for the ...
Duda Jozef
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Bounds of the matrix eigenvalues and its exponential by Lyapunov equation [PDF]
, 2012 summary:We are concerned with bounds of the matrix eigenvalues and its exponential. Combining the Lyapunov equation with the weighted logarithmic matrix norm technique, four sequences are presented to locate eigenvalues of a matrix.
Hu, Guang-Da, Mitsui, Taketomo
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Direct methods for matrix Sylvester and Lyapunov equations
Journal of Applied Mathematics, 2003 We revisit the two standard dense methods for matrix Sylvester and Lyapunov equations: the Bartels-Stewart method for A1X+XA2+D=0 and Hammarling's method for AX+XAT+BBT=0 with A stable.
Danny C. Sorensen, Yunkai Zhou
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Frontiers in Applied Mathematics and Statistics, 2019 System theory has its roots in mathematical formalisms developed by mathematicians and physicians, such as Leibniz, Euler and Newton, and applied by congenial ecologists and biologists such as Lotka and Bertalanffy.
W. Weckwerth
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The stability analysis of systems with nonlinear feedback expressed by a quadratic program [PDF]
, 2006 We consider the stability of the feedback connection of a stable linear time invariant (LTI) plant with a static nonlinearity expressed by a certain class of quadratic program (QP).
Lennox, B +5 more
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Lyapunov matrices approach to the parametric optimization of time-delay systems
Archives of Control Sciences, 2015 In the paper a Lyapunov matrices approach to the parametric optimization problem of time-delay systems with a P-controller is presented. The value of integral quadratic performance index of quality is equal to the value of Lyapunov functional for the ...
Duda Józef
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