Abstract
A new method for the parameter estimation of linear time-varying systems using Chebyshev polynomials of the second kind is presented. The systems are characterized by linear differential equations with time-varying coefficients that are in the form of polynomials in the time variable. The operational matrices of integration and time-variable multiplication of Chebyshev polynomials of the second kind play key roles in the derivation of the algorithm. Least-squares estimation of overdetermined linear algebraic equations obtained from polynomial approximations of the systems is used to estimate the unknown parameters. Illustrative examples give satisfactory results
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