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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 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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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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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 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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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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The Ψ−asymptotic equivalence of the Lyapunov matrix differential equations with modified argument [PDF]
ITM Web of Conferences, 2022 Using the notion of strict h−contraction, existence results for Ψ−asymptotic equivalence of two pairs of (Lyapunov) matrix differential equations with modified argument are given.
Diamandescu Aurel
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Novel Robust Stability Criteria for Uncertain Stochastic Neural Networks with Time-Varying Delay [PDF]
International Journal of Computational Intelligence Systems, 2009 This paper considers the robust stability analysis problem for a class of uncertain stochastic neural net- works with time-varying delay. Based on the Lyapunov functional method, and by resorting to the new technique for estimating the upper bound of the
Yunrui Guo, Yonggang Chen, Wenlin Li
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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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An efficient deep learning model for brain tumour detection with privacy preservation
CAAI Transactions on Intelligence Technology, EarlyView., 2023 Abstract Internet of medical things (IoMT) is becoming more prevalent in healthcare applications as a result of current AI advancements, helping to improve our quality of life and ensure a sustainable health system. IoMT systems with cutting‐edge scientific capabilities are capable of detecting, transmitting, learning and reasoning.
Mujeeb Ur Rehman +8 more
wiley +1 more source