Analysis of time-varying delay systems via triangular functions

Solution of linear time-varying multi-delay systems via variational iteration method

“…1. The results obtained via Lagrange polynomials [4], Triangular function [11] and adaptive Legendre-Gauss-Radau collocation method [17] are to that shown in Table 1. We mention in [17], N is the number of subintervals of the adaptive collocation method.…”

“…In general, the computation of the delay systems via orthogonal functions is not in good agreement with the exact response of the system [19]. Special attention has been given to such applications as Walsh functions [3], hybrid functions [4] and Triangular functions [11]. Special attention has been given to applications of wavelets [6], Adomian decomposition method (ADM) [2], homotopy perturbation method (HPM) [15], recurrent neural networks (RNN) [33] and others.…”

“…In particular, He [11] demonstrated an application of VIM to a first order delay differential equation (DDE) modeling a population growth model. Other researches have also demonstrated the power of this method.…”

A novel approach of fractional-order time delay system modeling based on Haar wavelet

“…When θ is not multiplier of h, discrete intervals can be obtained as ([0, θ], [θ, 2θ], …, [(N − 1)θ, Nθ]); where Nθ T f ⩾ and N can be chosen from Ref. [34],…”

Numerical solution of time-delay systems by Hermite wavelet

“…Uniquely, these matrices can be determined based on each orthogonal function. Orthogonal functions such as Walsh functions (Chen and Shih, 1978), block-pulse (Hsu and Cheng, 1981), Laguerre polynomials (Kung and Lee, 1983), Legendre polynomials (Lee and Kung, 1985), Chebyshev polynomial (Horng and Chou, 1985), triangular function (Hoseini and Soleimani, 2008), Bernstein polynomial (Yousefi and Behroozifar, 2010), hybrid of blockpulse functions and other polynomials (Maleknejad and Mahmoudi, 2004;Behroozifar and Yousefi, 2013) were used to derive the solution of such systems. Images in remote sensing often have properties that vary continuously in some regions and discontinuously in others.…”