In this article, the state-space symmetric systems with symmetrical interval uncertainty that have positive real and negative imaginary properties are studied. First, a necessary and sufficient test in view of a state matrix is derived for a state-space symmetric system to be negative imaginary, which allows having poles at the origin. Second, bounds on symmetrical interval uncertainty that guarantee the positive realness and negative imaginariness of state-space symmetric systems are provided. Finally, the main results are illustrated by a resistor–capacitor network and a numerical design example.
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