System analysis, parameter estimation and optimal regulator design of linear systems via Jacobi series

Abstract

The operational matrix of integration of a Jacobi vector whose elements are Jacobi polynomials is introduced and then applied to the analysis, parameter estimation and optimal regulator design of time-invariant linear systems. Illustrative examples are given for demonstration. Very satisfactory results are obtained due to rapid convergent property of the Jacobi series. The new method is algebraic and computer-oriented.