In this paper, we propose a new method to design an observer and control the linear singular systems described by Chebyshev wavelets. The idea of the proposed approach is based on solving the generalized Sylvester equations. An example is also given to illustrate the procedure.

In this paper, we consider the second-kind Chebyshev polynomials (SKCPs) for the numerical solution of the fractional optimal control problems (FOCPs). Firstly, an introduction of the fractional calculus and properties of the shifted SKCPs are given and then operational matrix of fractional integration is introduced. Next, these properties are used together with the Legendre-Gauss quadrature fo...

Fiedler pencils are a family of strong linearizations for polynomials expressed in the monomial basis, that include the classical Frobenius companion pencils as special cases. We generalize the definition of a Fiedler pencil from monomials to a larger class of orthogonal polynomial bases. In particular, we derive Fiedler-comrade pencils for two bases that are extremely important in practical ap...

The incomplete elliptic integral of the second kind, EðsinðTÞ;mÞ R T 0 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 m sinðT Þ q dT 0 where m 2 1⁄20;1 is the elliptic modulus, can be inverted with respect to angle T by solving the transcendental equation EðsinðTÞ;mÞ z 1⁄4 0. We show that Newton’s iteration, T 1⁄4 T EðsinðTÞ;mÞ z f g ffiffiffiffiffi...

1 Department of Mathematics, Islamic Azad University, Khorasgan Branch, 81515-158 Isfahan, Iran 2 Department of Mathematics, Khansar Faculty of Computer and Mathematics, University of Isfahan, Isfahan 81746-73441, Iran 3 Department of Physics, Faculty of Science, University PutraMalaysia, 43400 Serdang, Selangor, Malaysia 4 Department of Mathematics, Islamic Azad University, Mobarakeh Branch, 8...

In this paper, a special technique is studied by using the orthogonal Chebyshev polynomials to get approximate solutions for singular and hyper-singular integral equations of the first kind. A singular integral equation is converted to a system of algebraic equations based on using special properties of Chebyshev series. The error bounds are also stated for the regular part of approximate solut...

In this paper an accurate method to construct the bidiagonal factorization of collocation and Wronskian matrices Jacobi polynomials is obtained used compute with high relative accuracy their eigenvalues, singular values inverses. The particular cases Legendre polynomials, Gegenbauer Chebyshev first second kind rational are considered. Numerical examples included.