Solution of time-varying delay systems by hybrid functions

Application of Hybrid Functions for Solving Duffing-Harmonic Oscillator

“…wherẽcan be calculated in a similar way to matrix̃in (24). Since the above equation is satisfied for every ∈ [0, ), we can get…”

“…Razzaghi and Marzban [23] applied the hybrid of block-pulse and Chebyshev functions to find approximate solution of systems with delays in state and control. Solution of time-varying delay systems is approximated using hybrid of block-pulse functions and Legendre polynomials in [24]. Maleknejad and Tavassoli Kajani in [25] introduced a Galerkin method based on hybrid Legendre and block-pulse functions on interval [0, 1) to solve the linear integrodifferential equation system.…”

A Computational Approach to Vibration Control of Vehicle Engine-Body Systems

“…It has been applied in a wide range of engineering disciplines such as signal processing, pattern recognition and computational graphics. Recently, some of the attempts are made in solving surface integral equations, improving the finite difference time domain method, solving linear differential equations and nonlinear partial differential equations and modelling nonlinear semiconductor devices [5,6,7,13,16,17,18,21,27]. [13,16], Walsh functions [7], block pulse functions [27], Laguerre polynomials [14], Legendre polynomials [5], Chebyshev functions [12] and Fourier series [28], often used to represent an arbitrary time functions, have received considerable attention in dealing with various problems of dynamic systems.…”

“…Thus, the solution, identification and optimisation procedure are either greatly reduced or much simplified accordingly. The available sets of orthogonal functions can be divided into three classes such as piecewise constant basis functions (PCBFs) like HWs, Walsh functions and block pulse functions; orthogonal polynomials like Laguerre, Legendre and Chebyshev as well as sine-cosine functions in Fourier series [21].…”

Analysis of time-varying delay systems via triangular functions

“…In general, the computed response of the delay systems via orthogonal functions is not in good agreement with the exact response of the system [2]. Special attention has been given to applications of Walsh functions [3], block pulse functions [4], Laguerre polynomials [5], Legendre polynomials [6], Chebyshev polynomials [7], Haar wavelets [8], Fourier series [9] and hybrid functions [10,11].…”