Analysis of time-varying scaled systems via general orthogonal polynomials

General orthogonal polynomials are introduced to analyze and approximate the solution of a class of scaled systems. Using the operational matrix of integration, together with the operational matrix of linear transformation, the dynamical equation of a scaled system is reduced to a set of simultaneous linear algebraic equations. The coefficient vectors of the general orthogonal polynomials can be determined recursively by the derived algorithm. An illustrative example is given to demonstrate the validity and applicability of the orthogonal polynomial approximations.