On the correspondence of hyperbolic geometry and system analysis

Abstract

Abstract Different aspects of the relation between hyperbolic geometry and linear system theory are discussed in this paper. The underlying connection is presented by an intuitive example that points out the basic motivations. It is shown that the convergence factor of Laguerre series expansion is equal to the hyperbolic distance, under certain conditions. Preliminary results are also reported, connecting the H∞ norm and ν-gap metric with the hyperbolic distance. Furthermore, the equivalence of (i) the H∞ norm of the difference of two first order LTI system, (ii) the ν-gap of these systems and (iii) the hyperbolic distance is also proved, under specified assumptions.