Eigenvalue-Based Algorithms for Testing Negative Imaginariness of Scalar Transfer Functions

This paper proposes several algorithms based on eigenvalue computations for testing negative imaginariness of scalar transfer functions of single-input single-output time-invariant linear systems. The input of the proposed eigenvalue-based algorithms can be any state-space realization, not necessarily minimal. The algorithms can test negative imaginariness of descriptor systems whose transfer functions may be non-proper, and only involve eigenvalues computation of matrices or matrix pencils with fewer restrictions. Finally, illustrative examples are provided to show how the proposed eigenvalue-based algorithms are applied for negative imaginariness test.