On logarithmic complementary sensitivity integrals for MIMO systems

Bode and Poisson type integral inequalities for the complementary sensitivity function are derived in this paper for multi-input multi-output systems, which generalize earlier work of a similar nature but only applicable to single-input single-output systems. The results characterize how open loop nonminimum phase zeros may adversely affect a system´s performance, and how each of the zeros may couple with other nonminimum phase zeros and unstable poles to impose a severe limitation on the achievable performance quantified by the complementary sensitivity function, to which the zero directions are seen to play a central role