Analysis and parameter identification of linear systems via Chebyshev polynomials of the second kind

Abstract

The operational matrix for integration of the Chebyshev vector whose elements are Chebyshev polynomials of the second kind is derived. When the time function is approximated by Chebyshev series and the operational matrix of integration is applied, a linear differential equation can be represented by a set of linear algebraic equations. Parameter identification of time-invariant linear systems is also discussed using the gaussian integration formulae for Chebyshev polynomials of the second kind. Examples with satisfactory results are given.