Robust stability and performance analysis using LC multipliers and the Nyquist criterion

A previous approach to robust control design with real parameter uncertainty has been developed using nonlinear uncertainties and the analysis from absolute stability theory. In this work, the class of nonlinear functions considered in absolute stability theory are readily interpreted as system uncertainties, and thus can be incorporated within the standard modern robust control framework. Previous research has focused on several classes of nonlinearities, including time invariant, (odd) monotonic, and locally slope-restricted functions, to capture the real parameter uncertainty problem. The purpose of this note is to investigate absolute stability results for constant, real, linear uncertainties. For a single uncertainty, the results presented are necessary and sufficient for robust stability, and hence provide a Lyapunov function construction for the SISO Nyquist criterion.