Journal ArticleDOI
A new set of orthogonal functions and its application to the analysis of dynamic systems
TLDR
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 two-dimensional fuzzy Fredholm integral equations of the second kind using triangular functions
TL;DR: This paper uses fuzzy two-dimensional triangular functions to reduce the 2D–FFIE–2 to a system of linear Fredholm integral equations of the second kind with three variables in crisp and proves the convergence of the method.
Journal ArticleDOI
A new operational matrix for solving two-dimensional nonlinear integral equations of fractional order
TL;DR: In this article, the operational matrix of two-dimensional orthogonal triangular functions (2D-TFs) for 2D fractional integrals is derived and applied to a system of algebraic equations.
Journal ArticleDOI
Analysis of time-varying delay systems via triangular functions
TL;DR: A method for finding the analysis of time-varying delay systems using triangular functions using the operational matrices of integration, delay and product to reduce the solution of delay systems to the solutions of algebraic equations.
Journal ArticleDOI
Solving state feedback control of fractional linear quadratic regulator systems using triangular functions
TL;DR: Both left and right operational matrices of the triangular functions for arbitrary fractional order integral α > 0 in Caputo sense are applied to approximate solutions of fractional linear optimal control systems which have a quadratic performance index.
Journal ArticleDOI
An efficient hybrid method for solving fredholm integral equations using triangular functions
TL;DR: In this paper, the orthogonal triangular function (TF) based method is first applied to transform the Fredholm integral equations and Fredholm system of integral equations to a coupled system of matrix algebraic equations.
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.
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Zur Theorie der orthogonalen Funktionensysteme
TL;DR: In der Theorie der Reihenentwicklung der reellen Funktionen spielen die sog. orthogonalen Funktionensysteme eine fuhrende Rolle.
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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.