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This paper covers recent developments in the theory of negative imaginarysystems and their application to the control of highly resonant flexiblestructures. The theory of negative imaginary systems arose out of a desire tounify a number of classical methods for the control of lightly dampedstructures with collocated force actuators and position sensors includingpositive position feedback and integral force feedback. The key result is astability result which shows why these methods are guaranteed to yield robustclosed loop stability in the face of unmodelled spillover dynamics. Relatedresults to be presented connect the theory of negative imaginary systems topositive real systems theory and a negative imaginary lemma has beenestablished which is analogous to the positive real lemma. The paper alsopresents recent controller synthesis results based on the theory of negativeimaginary systems.

Negative Imaginary Systems Theory in the Robust Control of Highly Resonant Flexible Structures