Science Journal of Applied Mathematics and Statistics
Volume 3, Issue 4, August 2015, Pages: 194-198
Received: May 3, 2015;
Accepted: May 22, 2015;
Published: Jul. 29, 2015
Views 4312 Downloads 135
Mahmood Dadkhah, Department of Mathematics, PayameNoor University, Tehran, Iran
In this paper we present a method to find the solution of time-varying systems using orthonormal Bernstein polynomials. The method is based upon expanding various time functions in the system as their truncated orthonormal Bernstein polynomials. Operational matrix of integration is presented and is utilized to reduce the solution of time-varying systems to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.
Solving Linear Time Varying Systems by Orthonormal Bernstein Polynomials, Science Journal of Applied Mathematics and Statistics.
Vol. 3, No. 4,
2015, pp. 194-198.
A. Deb, A. Dasgupta, G. Sarkar, A new set of orthogonal functions and its application to the analysis of dynamic systems, J. Frank. Inst. 343, 1-26, 2006.
F. Khellat, S. A. Yousefi, The linear Legendre wavelets operational matrix of integration and its application, J. Frank. Inst. 343, 181-190, 2006.
F. Marcellan, and W.V. Assche, Orthogonal Polynomials and Special Functions (a Computation and Appli- cations), Springer-Verlag Berlin Heidelberg, 2006.
H. R. Marzban and M. Shahsiah, Solution of piecewise constant delay systems using hybrid of block- pulse and Chebyshev polynomials, Optim. Contr. Appl. Met., Vol. 32, pp. 647-659, 2011.
Kung, F. C. and Lee, H., Solution and parameter estimation of linear time-invariant delay systems using Laguerre polynomial expansion, Journal on Dynamic Systems, Measurement, and Control, 297-301, 1983.
LÃ¡zaro I, Anzurez J, Roman M, Parameter estimation of linear systems based on walsh series, The Electronics, Robotics and Automotive Mechanics Conference, 355-360, 2009.
M. H. Farahi, M. Dadkhah, Solving Nonlinear Time Delay Control Systems by Fourier series, Int. Journal of Engineering Research and Applications, Vol. 4, Issue 6 , 217-226, 2014.
M. I. Bhatti and P. Bracken, Solutions of differential equations in a Bernstein polynomial basis, Journal of Computational and Applied Mathematics, 205, 272 -280, 2007.
M. Sezer, and A.A. Dascioglu, Taylor polynomial solutions of general linear differential-difference equations with variable coefficients, Appl. Math.Comput.174, 1526-1538, 2006.
M. Shaban and S. Kazem and J. A. Rad, A modification of the homotopy analysis method based on Chebyshev operational matrices, Math. Comput. Model, in press(2013)
Richard A. Bernatz. Fourier series and numerical methods for partial defferential equations. John Wiley & Sons, Inc., New York, 2010.
S. A. Youseï, M. Behroozifar, Operational matrices of Bernstein polynomials and their applications, Int. J. Syst. Sci. 41, 709-716, 2010.
Wang, X., T, Numerical solutions of optimal control for time delay systems by hybrid of block-pulse functions and Legendre polynomials Applied Mathematics and Computation, 184, 849-856, 2007.
Z.H. Jiang, W. Schaufelberger, Block Pulse Functions and Their Applications in Control Systems, Springer-Verlag, 1992.