Algebraic Stability Analysis and Stabilization by Proportional Controllers: Critical Inflection Point in Phase Diagram

This paper deals with algebraic stability analysis and investigating the existence of proportional stabilizing controllers on the basis of frequency response data. Firstly, it is shown that using the available results in this subject may yield in inconsistent subsequences in the cases that there is a critical inflection point in phase diagram of the open-loop/process transfer function. Then, to solve this inconsistency problem some modifications are proposed. Finally, conditions for ensuring the existence of critical inflection point in phase diagram of a dynamical system are analytically found.