© The Institution of Electrical Engineers
Applications of the shifted Legendre polynomials expansion to the analysis and identification of the nonlinear timedelayed system, described by a memoryless nonlinear element followed by a linear plant with time delay, are studied. The system described here is assumed both controllable and observable. For analysis, by using the shifted Legendre polynomials expansion, the solution of a nonlinear state equation is reduced to the solution of a linear algebraic matrix equation. For identification, through the shifted Legendre expansions of the measured input/output data, the unknown parameters of both the linear delayed plant and the characterisation of the nonlinear element are estimated by using the leastsquares method. Algorithms are presented. Numerical examples are given to illustrate the use of this approach.
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