State-Space Representation and Stability Analysis of Time-Domain GSTC-Based Metasurface Solvers

A continuous-time state-space formulation is pre-sented to analyze the stability and poles of the analytical Generalized Sheet Transition Conditions (GSTC) that characterize idealized metasurfaces. Furthermore, a discrete-time state-space formulation is also presented to analyze the numerical stability when the GSTC is discretized using a finite difference scheme in the time domain. A bilinear transform is applied to map between the continuous-time and discrete-time domains to examine the influence of finite time discretization to the poles and stability of the GSTC.