Novel characterization of the infimum in ℋ∞ full information control of discrete-time plants

The Toeplitz Corona Theorem characterizes the infimal ¿_¿ norm of a systems right inverses in terms of a Toeplitz operators smallest singular value. Recently, it has been shown that the finite section method can be used to approximate this infimal ¿_¿ norm. In this paper, we point out that these results can also be used to approximate the limit of the gamma iteration in discrete-time ¿_¿ full information control. The approximations can be made arbitrarily close. They have the nice property that they are always lower bounds on the exact value. Their computation is simple and numerically reliable. Furthermore, our results are quite general. They in particular include control problems where the D₂ matrix is rank deficient. We only assume that the sub-plant (A, B₂, C, D₂) has full column rank on the unit circle.