Stabilization of uncertain negative-imaginary systems using a Riccati equation approach

In this paper, a stabilization procedure that forces an uncertain system to be stable and satisfy the negative imaginary property is presented. The controller synthesis procedure is based on the negative imaginary lemma. As a result, the closed-loop system can be guaranteed to be robustly stable against any strict negative imaginary uncertainty, such as in the case of unmodeled spill-over dynamics in a lightly damped flexible structure. A numerical example is presented to illustrate the usefulness of the proposed results.