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KRYLOV SUBSPACE METHODS FOR SOLVING LARGE LYAPUNOV EQUATIONS [PDF]
, 1994 Published ...
KASENALLY, EM, JAIMOUKHA, IM
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On the Ψ−uniform asymptotic stability of nonlinear Lyapunov matrix differential equations [PDF]
ITM Web of Conferences, 2022 This paper deals with obtaining (necessary and) sufficient conditions for Ψ− uniform asymptotic stability of solutions of nonlinear Lyapunov matrix differential equations.
Diamandescu Aurel
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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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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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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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A Hill-Pick matrix criterion for the Lyapunov order
Journal of Mathematical Analysis and Applications, 2022 The Lyapunov order appeared in the study of Nevanlinna-Pick interpolation for positive real odd functions with general (real) matrix points. For real or complex matrices $A$ and $B$ it is said that $B$ Lyapunov dominates $A$ if \begin{equation*} H=H^*,\quad HA+A^*H \geq 0 \quad \implies \quad HB+B^*H \geq 0.
S. ter Horst, A. van der Merwe
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Lyapunov Matrices Approach to the Parametric Optimization of a System with Two Delays
Archives of Control Sciences, 2016 In the paper a Lyapunov matrices approach to the parametric optimization problem of time-delay systems with two commensurate delays and a P-controller is presented. The value of integral quadratic performance index of quality is equal to the value of the
Duda Jozef
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Error analysis of QR algorithms for computing Lyapunov exponents [PDF]
, 2001 Lyapunov exponents give valuable information about long term dynamics. The discrete and continuous QR algorithms are widely used numerical techniques for computing approximate Lyapunov exponents, although they are not yet supported by a general error ...
McDonald, E.J., Higham, D.J.
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Journal of High Energy Physics, 2019 We introduce a simple quantum generalization of the spectrum of classical Lyapunov exponents. We apply it to the SYK and XXZ models, and study the Lyapunov growth and entropy production.
Hrant Gharibyan +3 more
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