Journal ArticleDOI
A new set of orthogonal functions and its application to the analysis of dynamic systems
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It has been established with illustration that the TF domain technique is more accurate than the BPF domain technique as far as integration is concerned, and it provides with a piecewise linear solution.Abstract:
The present work proposes a complementary pair of orthogonal triangular function (TF) sets derived from the well-known block pulse function (BPF) set. The operational matrices for integration in TF domain have been computed and their relation with the BPF domain integral operational matrix is shown. It has been established with illustration that the TF domain technique is more accurate than the BPF domain technique as far as integration is concerned, and it provides with a piecewise linear solution. As a further study, the newly proposed sets have been applied to the analysis of dynamic systems to prove the fact that it introduces less mean integral squared error (MISE) than the staircase solution obtained from BPF domain analysis, without any extra computational burden. Finally, a detailed study of the representational error has been made to estimate the upper bound of the MISE for the TF approximation of a function f ( t ) of Lebesgue measure.read more
Citations
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Journal ArticleDOI
Numerical solution of fractional differential equations using the generalized block pulse operational matrix
Yuanlu Li,Ning Sun +1 more
TL;DR: A way to solve the fractional differential equations using the Riemann-Liouville fractional integral for repeated fractional integration and the generalized block pulse operational matrices of differentiation are proposed.
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Numerical solution of nonlinear Volterra-Fredholm integro-differential equations via direct method using triangular functions
TL;DR: An effective direct method to determine the numerical solution of the specific nonlinear Volterra-Fredholm integro-differential equations is proposed, based on new vector forms for representation of triangular functions and its operational matrix.
Journal ArticleDOI
Triangular functions (TF) method for the solution of nonlinear Volterra–Fredholm integral equations
TL;DR: A numerical method based on an m-set of general, orthogonal triangular functions (TF) is proposed to approximate the solution of nonlinear Volterra-Fredholm integral equations.
Journal ArticleDOI
Two-dimensional triangular functions and their applications to nonlinear 2D Volterra-Fredholm integral equations
TL;DR: Two-dimensional orthogonal triangular functions are presented as a new set of basis functions for expanding 2D functions and used to approximate solutions of nonlinear two-dimensional integral equations by a direct method.
Journal ArticleDOI
Using triangular orthogonal functions for solving Fredholm integral equations of the second kind
TL;DR: The present work proposes a method for solving Fredholm integral equations using a complementary pair of orthogonal triangular functions set derived from the well-known block pulse functions set, and demonstrates validity and applicability of the method.
References
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Journal ArticleDOI
Analysis and synthesis of dynamic systems via block-pulse functions
TL;DR: The paper presents a method of numerically integrating a system of differential equations based on an idea of orthogonal approximation of functions that gives piecewise constant solutions with minimal mean-square error and is computationally similar to the familiar trapezoidal rule of integration.
Book
Block pulse functions and their applications in control systems
TL;DR: This research presents a new generation of block pulse operational matrices for integrations that combine nonparametric representations of dynamic systems with state space representations ofynamic systems.
Journal ArticleDOI
Analysis and synthesis of dynamic systems containing time delays via block-pulse functions
Ganti Prasada Rao,T. Srinivasan +1 more
TL;DR: In this article, the authors present a method of numerically integrating differential equations containing time delays via block-pulse functions, and the resulting solutions are piecewise constant with minimal mean square error.
Journal ArticleDOI
Block pulse functions, the most fundamental of all piecewise constant basis functions
TL;DR: In this article, it is shown that block pulse functions (BPFs) are superior to the delayed unit step function (DUSF) proposed by Hwang (1983) due to the most elemental nature of BPFs in comparison to any other PCBF function.
Journal ArticleDOI
A new set of piecewise constant orthogonal functions for the analysis of linear siso systems with sample-and-hold
TL;DR: In this paper, a set of piecewise constant orthogonal functions, termed sample-and-hold functions (SHF), is introduced for the analysis of control systems with SISO.