Stabilization of Conditional Uncertain Negative-imaginary Systems Using Riccati Equation Approach

In this paper, we derive a negative imaginary and a strict negative imaginary lemma based on Riccati equations. The resulting negative imaginary lemma is used to solve a controller synthesis problem. For a given uncertain system, a static controller is constructed to force the system to satisfy the negative imaginary property. 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.