Finite and Infinite Horizon Fixed-order Lqg Compensation Using the Delta Operator

The strengthened discrete-time optimal projection equations (SDOPE) are presented in a form based on the delta operator. This form unifies discrete-time and continuous-time results. Based on this unification, recently established results and algorithms for finite and infinite-horizon fixed-order LQG compensation of discrete-time systems are carried over to the continuous-time case. The results concern the equivalence of the strengthened optimal projection equations to first-order necessary optimality conditions together with the condition that the compensator is minimal. Furthermore in the finitehorizon continuous-time case the problem of stating the optimal projection equations explicitly in the LQG problem parameters is explained and resolved. The algorithms exploit the resemblance between the strengthened optimal projection equations and the Riccati equations of full-order LQG control. They allow for efficient numerical computation of fixed-order LQG compensators through repeated forward and backward iteration (integration) of the SDOPE. They are illustrated with four numerical examples.