Frequency Analysis of Uncertain System

This paper is dedicated to the study and analysis of a successfully designed control system, whose capability should always maintain the stability and performance level in spite of the uncertainties in system dynamics and within the working environment to a certain degree. Design requirements such as gain margin and phase margin in using classical frequency-domain techniques are solely for the purpose of robustness. A constrained optimization is then performed to maximize the robust stability of the closed-loop system to the type of uncertainty chosen, the constraint being the internal stability of the feedback system. In most cases, it would be sufficient to search a feasible controller such that the closed-loop system should achieve certain robust stability. Performance objectives can also be included in the optimization cost function. Elegant solution formulae have been developed, which are based on the solutions of certain Algebraic Riccati Equations