Generalized positiveness of spatially interconnected systems over quadratically constrained frequency domains

Generalized positiveness is investigated in this paper for a spatially interconnected system (SIS). Results of [7] are corrected and extended to a more general frequency domain and to more complicated requirements on the frequency response of a SIS. Based on an equivalent characterization of the interested frequency domain, a linear matrix inequality (LMI) based sufficient condition is derived for the generalized positiveness of a SIS over a frequency domain described by several matrix valued quadratic functions. Moreover, using the separability property of convex sets, situations have also been clarified under which this sufficient condition becomes also necessary.