Performance limitations in the robust servomechanism problem for sampled LTI systems

Abstract

Fundamental limitations for error tracking/regulation are obtained for the robust servomechanism problem (RSP) for a sampled system. In studying this problem, the cheap control problem for a multi-input/multi-output discrete time system is considered, and explicit expressions are obtained for the limiting steady state solution of its associated algebraic Riccati equation (ARE), as the weight on the control energy tends to zero. Application of these results is then made to the “sampled system cheap robust servomechanism problem”, and explicit expressions for the limiting costs for error tracking regulation are obtained. These limitations can he characterized completely by the number and location of the unstable transmission zeros.