Fundamental Limits in Robustness and Performance for Unstable, Underactuated Systems

Abstract

We derive bounds on the H∞ norm of a weighted output sensitivity function and weighted output complementary sensitivity function for an underactuated, multiple input/multiple output, linear, time-invariant (LTI), unstable plant in feedback with an internally stabilizing, LTI controller. These bounds indicate a limit to the achievable robustness and performance for such systems and thus, are valuable tools for performing system design trade-offs.