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Abstract: Negative-imaginary systems have important engineering applications, for example, in lightly damped flexible structures with collocated position sensors and force actuators. This paper proposes a new Negative-Imaginary Lemma for generalized negative-imaginary systems, where the minimality assumption is relaxed. The proposed lemma facilitates both analysis and synthesis for negative-imaginary systems. Invoking this result, a systematic robust static state-feedback synthesis method is proposed in an LMI framework for systems with strictly negative-imaginary uncertainty (e.g. unmodeled spill-over dynamics in a lightly damped flexible structure) assuming all states are available for state feedback. Two numerical examples are given to show the usefulness of the proposed results. [Copyright &y& Elsevier]