U-D factorisation of the strengthened discrete-time optimal projection equations

Abstract

Algorithms for optimal reduced-order dynamic output feedback control of linear discrete-time systems with white stochastic parameters are U-D factored in this paper. U-D factorisation enhances computational accuracy, stability and possibly efficiency. Since U-D factorisation of algorithms for optimal full-order output feedback controller design was recently published by us, this paper focusses on the U-D factorisation of the optimal oblique projection matrix that becomes part of the solution as a result of order-reduction. The equations producing the solution are known as the optimal projection equations which for discrete-time systems have been strengthened in the past. The U-D factored strengthened discrete-time optimal projection equations are presented in this paper by means of a transformation that has to be applied recursively until convergence. The U-D factored and conventional algorithms are compared through a series of examples.