Optimal State-Space Realizations of Digital Controllers with Roundoff Noise Consideration

The effect of roundoff noise in a state-space digital controller is investigated for a discrete-time control system. An analytical expression of the roundoff noise gain is obtained, with which the optimal realization problem is solved on the set of fully parametrized realizations. A sparse structure is derived and analyzed in terms of roundoff noise performance. The problem of finding optimized sparse structures is solved. A design example is given, which shows that the optimized sparse realization beats the fully parametrized optimal realization in terms of roundoff noise gain and computation efficiency.