L2 disturbance attenuation and performance bounds for linear non-minimum phase square invertible systems

A complete solution, including explicit performance bounds, is provided, to the problem of finding a state feedback that asymptotically stabilizes the system and achieves disturbance attenuation (in the sense of the L₂ gain), for square invertible linear systems. The solution exposes the intimate relationship between the unstable forced zero dynamics of the system and the ability to disturbance attenuate. Further, we derive, using relatively simple techniques a sufficient condition for almost disturbance decoupling with a stability margin. The condition thus found actually coincides with the condition given by Willems (1981) and Weiland and Willems (1989), which was proven to be necessary and sufficient