A new approach to the parameter estimation of linear time-invariant delayed systems via modified Laguerre polynomials

Abstract

The conventional Laguerre polynomials are modified with an additional parameter and is then applied to solve the dynamic linear time-invariant delayed system. The problem of parameter estimation for such a system is also studied by using the modified Laguerre polynomials. A new approach, which is the extension of Laguerre polynomials to fractional calculus, is proposed in calculating the expansion coefficients of the state function. The recursive computational calculation procedure is easy and straightforward. Tedious iterative algorithms and direct matrix inversion for large-scale systems are thus avoided in calculating the expansion coefficients. The proposed method is more effective than those previously documented. Very satisfactory results are obtained by the proposed method when compared with exact solutions.