H∞ model reduction for negative imaginary systems

ABSTRACT This paper is concerned with the H∞ model reduction for negative imaginary (NI) systems. For a given linear time-invariant system that is stable and NI, our goal is to find a stable reduced-order NI system satisfying a pre-specified H∞ approximation error bound. Sufficient conditions in terms of matrix inequalities are derived for the existence and construction of an H∞ reduced-order NI system. Iterative algorithms are provided to solve the matrix inequalities and to minimise the H∞ approximation error. Finally, a numerical example is used to demonstrate the effectiveness of the proposed model reduction method.

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