Fundamental Limitations of Monotonic Tracking Systems

Abstract

We consider the monotonic tracking control problem for continuous-time single-input single-output linear systems using output-feedback linear controllers in this article. We provide the necessary and sufficient conditions for this problem to be solvable and expose its fundamental limitations: the exact feasible locations of the plant zeros, the minimum controller order possible, and the fastest decay rate achievable for the closed-loop system. The relationship between these bounds is explained by a simple geometric shape for plants with a pair of complex-conjugate zeros.