Extended argument principle and integral design constraints. Part I. A unified formula for classical results

We study Bode and Poisson type integral relations. We focus on a link between the well-known argument principle and Bode and Poisson integrals, which have been unnoticed previously. We show how various integral constraints may be unified under an extended version of the argument principle. This enables us to derive the classical Bode and Poisson integral relations in a simple manner, and further to discover new integral formulas of significance for an analysis of control design limitation and tradeoff.