Argument Principle and Integral Relations: Hidden Links and Generalized Forms

Abstract

This article studies Bode/Poisson type sensitivity and complementary sensitivity integral relations for linear, time-invariant feedback control systems. We call for attention to a seemingly unnoticed link between the well-known argument principle and Bode/Poisson integral relations. In this respect, a generalized version of the argument principle is developed, under which it is shown that various Bode/Poisson type integral relations can be unified, and new integral relations can be derived. The new and classical integral relations together provide useful insights for analyzing control design limitations and tradeoffs.