The structure of characteristic values for classes of linear time-invariant systems

In this paper, a particular structure of the characteristic values found in some classes of systems is dealt with. In particular, for the linear time-invariant systems in minimal form (A, B, C, D) with transfer function matrix G(s) for which if μi is a characteristic value, then also (Formula presented.) is. Consequently, when the system order is odd, a singular value is equal to one. The classes of systems for which this property holds are characterised by the existence of specific state-space representations. Moreover, the same structure of the characteristic values can be also retrieved for the class of even, (G(s) = GT(−s)), and odd (G(s) = −GT(−s)) systems. Several examples related to Multi Input Multi Output (MIMO) systems are reported, also referring to real physical systems.