Analysis of Time-delay Systems via Hybrid of Block-pulse Functions and Taylor Series

2005 ◽  
Vol 11 (12) ◽  
pp. 1455-1468 ◽  
Author(s):  
H. R. Marzban ◽  
M. Razzaghi
Keyword(s):  
Time Delay ◽  
Taylor Series ◽  
Delay Systems ◽  
Operational Matrices ◽  
Time Delay Systems ◽  
Algebraic Equations ◽  
Hybrid Functions ◽  
Block Pulse Functions ◽  
Hybrid Function

In this paper we present a method for finding the solution of time-delay systems using a hybrid function. We present the properties of the hybrid functions, which consist of block-pulse functions plus Taylor series. The method is based upon expanding various time functions in the system as their truncated hybrid functions. Operational matrices of integration and delay are presented and are utilized to reduce the solution of time-delay systems to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

scholarly journals A hybrid domain analysis for systems with delays in state and control

2001 ◽  
Vol 7 (4) ◽  
pp. 337-353 ◽  
Author(s):  
M. Razzaghi ◽  
H. R. Marzban
Keyword(s):  
Time Delay ◽  
Operational Matrix ◽  
Delay Systems ◽  
Operational Matrices ◽  
Time Delay Systems ◽  
Algebraic Equations ◽  
Hybrid Functions ◽  
Hybrid Domain ◽  
Block Pulse Functions ◽  
And Control

The solution of time-delay systems is obtained by using a hybrid function. The properties of the hybrid functions consisting of block-pulse functions and Chebyshev polynomials are presented. The method is based upon expanding various time functions in the system as their truncated hybrid functions. The operational matrix of delay is introduced. The operational matrices of integration and delay are utilized to reduce the solution of time-delay systems to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

scholarly journals Numerical Solution of Nonlinear Fredholm Integrodifferential Equations of Fractional Order by Using Hybrid Functions and the Collocation Method

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Jianhua Hou ◽  
Beibo Qin ◽  
Changqing Yang
Keyword(s):  
Numerical Solution ◽  
Integral Equations ◽  
Taylor Series ◽  
Fredholm Integral Equations ◽  
Algebraic Equations ◽  
Numerical Examples ◽  
Hybrid Functions ◽  
Block Pulse Functions ◽  
Hybrid Function ◽  
Nonlinear Fredholm Integral Equations

A numerical method to solve nonlinear Fredholm integral equations of second kind is presented in this work. The method is based upon hybrid function approximate. The properties of hybrid of block-pulse functions and Taylor series are presented and are utilized to reduce the computation of nonlinear Fredholm integral equations to a system of algebraic equations. Some numerical examples are selected to illustrate the effectiveness and simplicity of the method.

scholarly journals Solution of the Nonlinear Mixed Volterra-Fredholm Integral Equations by Hybrid of Block-Pulse Functions and Bernoulli Polynomials

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
S. Mashayekhi ◽  
M. Razzaghi ◽  
O. Tripak
Keyword(s):  
Numerical Method ◽  
Integral Equations ◽  
Bernoulli Polynomials ◽  
Fredholm Integral Equations ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Hybrid Functions ◽  
Block Pulse Functions

A new numerical method for solving the nonlinear mixed Volterra-Fredholm integral equations is presented. This method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The operational matrices of integration and product are given. These matrices are then utilized to reduce the nonlinear mixed Volterra-Fredholm integral equations to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

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