Analysis and optimal control of time-varying linear systems via shifted Legendre polynomials

Abstract

This paper extends the application of shifted Legendre polynomial expansion to time-varying systems. The extension is achieved through representing the product of two shifted Legendre series in a new shifted Legendre series. With this treatment of the product of two time functions, the operational properties of the shifted Legendre polynomials are fully applied to the analysis and optimal control of time-varying linear systems with quadratic performance index.