Fundamental limits in robustness and performance for unstable, underactuated systems

We derive bounds on the /spl Hscr//sub /spl infin// norm of a weighted output sensitivity function and a weighted output complementary sensitivity function for an underactuated, multiple-input-multiple-output (MIMO), 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 tradeoffs.