Analysis and parameter identification of bilinear systems via shifted Legendre polynomials
Chyi Hwang, Muh-Yang Chen · International Journal of Control · 1986
A new method of solving problems of analysis and parameter identification of bilinear systems via shifted Legendre polynomials is presented. It is based on treating the product of two time functions as a single function. Therefore, the shifted Legendre coefficient vector of this product function may be represented in terms of those of its component functions. This representation enables the transformation of given differential equations with variable coefficients to a computationally convenient matrix-algebraic form. This matrix algebraic form may then be used to find the expansion coefficients vectors of unknown functions or to determine the unknown parameters of bilinear systems.