Multivariable Euler transform of systems of linear ordinary differential equations of Okubo normal form

Yokoyama, Toshiaki

doi:10.1007/s11139-015-9753-1

Cited by 2 publications

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“…A case study for solving the long-term voltage instability problem in active distribution networks is studied in the literature [16]. The dimensionality problem of the corresponding homogeneous problem in the space of nonzero solutions and the oscillatory behavior of the nonzero solutions on the interval [a,b] are studied, and the literature [17][18] on sufficient conditions for the effective solvability of the nonhomogeneous problem is established.…”

Section: Introductionmentioning

confidence: 99%

Application of linear ordinary differential equations to the stability control of long time lag networks

Yao

2023

Applied Mathematics and Nonlinear Sciences

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Optimal control based on the exact synchronization of linear ordinary differential equations can provide conditions for the existence of optimal control of long-time lag network stability. In this paper, we first generalize network control systems, time lag systems, and modern control system stability theory to discuss long-time lag network stability analysis and control problems. The numerical solution method for solving ordinary differential equations with boundary conditions is proposed by combining the numerical solution method for initial value problems of differential equations and the iterative method for solving nonlinear equations. Finally, the fixed-time synchronization problem of complex networks with time-varying time lags under periodic intermittent control is studied. Two intermittent control strategies are designed based on the linear ordinary differential equation algorithm, and the convergence analysis of the synchronization error and the synchronization criterion are given. Numerical values show that the synchronization error converges to zero (< 1.0e − 5) in 0.32s, while the convergence times are 0.55s and 0.90s. The fixed times of the three methods are calculated to be T * = 0.52, T 1 = 0.71 and T 2 = 1.32, respectively, and the synchronization error system converges faster under the method in the paper. The numerical simulation results verify the effectiveness of linear ordinary differential equations in controlling the stability of long-time lag networks.

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Section: Introductionmentioning

confidence: 99%