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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Proceedings ArticleDOI
Numerical algorithm for the solution of third order differential equations in orthogonal hybrid function (HF) domain
TL;DR: In this paper, the authors proposed a new set of orthogonal hybrid functions (HF) which evolved from synthesis of Orthogonal Sample-and-Hold functions (SHF) and triangular functions (TF).
Book ChapterDOI
Function approximation via hybrid functions
TL;DR: In this paper, a modified approach, named HFm approach, seems to be more accurate than the conventional HF domain technique, termed as HFc approach, and error estimates for the SHF domain approximation and TF domain approximation are derived.
Journal Article
A Numerical Method For Solving Physiology Problems By Shifted Chebyshev Operational Matrix
E. Hashemizadeh,Firooz Mahmoodi +1 more
TL;DR: In this article, a new numerical solution of singular nonlinear differential equations, stemming from biology and physiology problems, is proposed, which is primarily based on the shifted Chebyshev polynomials operational matrix of derivative and collocation.
Journal ArticleDOI
Calculation of electric charge density based on a numerical approximation method using triangular functions
TL;DR: In this paper, the authors used vector forms of triangular functions to reduce the solution of an integral equation into solving a system of algebraic equations, which is based on an existing numerical method that has previously been proposed for solving some electromagnetic scattering problems.
References
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Book
Modern control engineering
TL;DR: This comprehensive treatment of the analysis and design of continuous-time control systems provides a gradual development of control theory and shows how to solve all computational problems with MATLAB.
Journal ArticleDOI
Zur Theorie der orthogonalen Funktionensysteme
TL;DR: In der Theorie der Reihenentwicklung der reellen Funktionen spielen die sog. orthogonalen Funktionensysteme eine fuhrende Rolle.
Journal ArticleDOI
Identification of continuous-time systems
G.P. Rao,Heinz Unbehauen +1 more
TL;DR: Continuous-time model-based system identification as mentioned in this paper is a well-established field in the field of control systems and is concerned with the determination of particular models for systems that are intended for a certain purpose such as control.
Journal ArticleDOI
Walsh operational matrices for fractional calculus and their application to distributed systems
C.F. Cheng,Y.T. Tsay,Tao Wu +2 more
TL;DR: In this paper, the Walsh operational matrix for performing integration and solving state equations is generalized to fractional calculus for investigating distributed systems and a new set of orthogonal functions is derived from Walsh functions.