Sensitivity limitations for multivariable linear filtering

This paper examines limitations in performance which apply to state estimators for square, linear multivariable systems. These limitations, involving the sensitivity of state estimates to process and measurement disturbances, result from interpolation constraints imposed by open right half-plane poles and zeros in the transfer matrices linking process noise and output noise to state estimates. Using the Poisson integral inequality, this paper shows how sensitivity limitations and tradeoffs in multivariable filtering problems are related to the directionality properties of the open right half-plane poles and zeros in these transfer matrices