Analysis and optimal control of linear time-varying systems via general orthogonal polynomials
Shuh‐Chuan Tsay, Tsu‐Tian Lee · International Journal of Systems Science · 1987
The operational matrix consisting of the product of two time functions, and the operational matrices for forward or backward integration consisting of general orthogonal polynomials are derived, respectively, for the analysis and optimal control of linear time-varying systems with a quadratic performance measure. The present results include results obtained via Chebyshev, Legendre, Laguerre, Jacobi, Hermite and ultraspherical polynomials as special cases.