USING A FUNCTIONAL-INTEGRATION MATRIX TO SOLVE TIME-VARYING BILINEAR-SYSTEMS

The Fourier series approximation approach is employed to analyse time-varying bilinear systems. The functional integration matrix and coefficient matrix of the Fourier series are derived first. The functional integration matrix is used to fulfill the integration process and transform the initial condition to the matrix equation. The product of two truncated functions is replaced by a concise form through the coefficient matrix. The numerical model is derived from the original differential equation based on matrix algebra. An example is illustrated to show the usage of this study, and the results are compared with traditional Fourier series approach and Runge-Kutta method.