Polynomial LQG regulator design for general system configurations

A polynomial-equation approach to the linear quadratic Gaussian (LQG) regulation problem for a general system configuration is presented. The solution is given in terms of a left-spectral factorization plus a pair of bilateral Diophantine equations. The resulting control-design procedure is based on an innovations representation of the system. This can be obtained from a physical description by solving, via polynomial equations, a minimum mean-square error filtering problem. The use in cascade of the above two procedures allows one to generalize previous polynomial design results to general system configurations