Infinite-Dimensional Negative Imaginary Systems

Abstract

We consider second order infinite-dimensional systems with force control and collocated position measurement interconnected with finite-dimensional controllers of the same type. We show that under assumptions that generalize those in the finite-dimensional case (the theory of negative imaginary systems), asymptotic stability of the closed-loop system can be concluded, but that the closed-loop system may not be exponentially stable nor input-output stable.