Analysis of robust performance for uncertain negative-imaginary systems using structured singular value

Negative-Imaginary systems are important in engineering practise as this class of systems quite often appears in practical problems, for example, lightly damped flexible structures with collocated position sensors and force actuators. In this paper, the problem of assessing the robust ℋ∞ performance of uncertain negative-imaginary systems is investigated. It is shown that a structure singular value condition for a transformed input/output map equivalently gives a quantitative performance (measured via an ℋ∞-norm) test for systems with strictly negative-imaginary uncertainty.