A construction of multiple input multiple output non-proper negative imaginary systems: based on Weyl's inequality

In this paper, we focus on multiple input multipleoutput non-proper negative imaginary systems whose transfer functions are non-proper matrix-valued real-rational functions. Our aim is to provide sufficient coefficient-based conditions for constructing non-proper negative imaginary systems with relative order −1 or −2. These main results are related to maximum and minimum eigenvalues of transfer functions' coefficient matrices based on Weyl's inequalities. Moreover, by applying the coefficient-based conditions, we can construct interval negative imaginary systems. Some examples are also provided to illustrate the main results.