Abstract
This paper addresses two open problems in the area of model reduction for negative imaginary systems. The first one is the H 2 model reduction problem for stable negative imaginary systems, and the second one is the mixed H 2 /H ∞ model reduction problem. Sufficient conditions in terms of matrix inequalities are derived for the existence and construction of H 2 and mixed H 2 /H ∞ reduced-order negative imaginary systems. Iterative algorithms are provided to solve the matrix inequalities and to minimize the H2 approximation error. Finally, numerical examples are used to demonstrate the effectiveness of the proposed model reduction methods.
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