H2 and Mixed H2/H∞ Model Reduction for Negative Imaginary Systems

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-infinity 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-infinity reduced-order negative imaginary systems. Iterative algorithms are provided to solve the matrix inequalities and to minimize the H-2 approximation error. Finally, numerical examples are used to demonstrate the effectiveness of the proposed model reduction methods.