Design tools for electrochemical supercapacitors using local absolute stability theory

In this paper, system properties of a physics-based model of a supercapacitor are computed using a local Lyapunov analysis and the solution of linear matrix inequalities. By considering the model as a Lurie system, bounds are computed for the resistance, capacitance, stored and dissipated energies for a charging profile, model stability, maximum reachable set with an input current impulse and the maximum voltage such that the potential difference across the double layer never exceeds the electrolyte overpotential. The bounds computed in this paper will aid the designers of supercapacitors, as the effect on the system properties caused by changes to the physical parameters can now be estimated. The theoretical results predicted by the analysis are compared against experimental data.