A method of model reduction for reducing a higher order transfer function to its lower order model is developed based on the shifted Legendre function approximation. The expansion coefficients of the shifted Legendre series which represents the approximate responses of transfer functions are computed by the recursive formula, via operational matrix approach. The significances of applying shifted Legendre function to model reduction problem are that the method is simple, straightforward and the computational results obtained are accurate as well as the final time of the control system can be adjustable without any restriction. Based on the model reduction technique, a new algebraic method is proposed for the design of a feedback control system to satisfy specifications. Illustrative examples are given and satisfactory results are obtained.

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