Although Convex Invertible Cones (CICs) may seem to be algebraically peculiar, they naturally appear in stability analysis of continuous-time physical systems. In this talk we explore samples of CICs from system theory and establish inter-connections among them. To name but three: Positive real rational functions, sets of matrices sharing common Lyapunov factor, sets of realization arrays. As time permits, applications and open problems will be presented.
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