Shifted Popov criterion and stability analysis of fuzzy control systems

The authors derive a shifted Popov criterion, which bridges the gap between the Popov and circle criteria. This criterion is applicable to nonlinear feedback systems whose nonlinearity consists of the main term and deviation term, where the main term is time-invariant and depends only on the output of the linear part, but the deviation term is time-varying and/or depends on variables other than the output. The proof of the theorem uses a lemma obtained in the composite-system analysis as well as a special form of the positive-real lemma. To show the practical significance of the new criterion, a certain type of fuzzy control system is analyzed