Integral constraints and performance limits on complementary sensitivity: discrete-time systems

We study performance limitation issues for multivariable discrete-time feedback systems. The complementary sensitivity function is employed as a performance measure, and Bode and Poisson-type integral inequalities and H(infinity)-type performance limits are derived. The results exhibit Frequency-dependent constraints as well as best achievable limits on the complementary sensitivity function, which are shown to be determined by nonminimum phase zeros, unstable poles, and time delays. In particular, the directions of such zeros and Dotes are seen to play a central role to this effect. (C) 2000 Elsevier Science B.V. All rights reserved.