Determination of Gain and Phase Margins in Lur’e Nonlinear Systems using Extended Circle Criterion

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Delavar Abolfazl; Haeri Mohammad

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Journal Paper

Paper Information

Journal: Journal of Control Year:2022 | Volume:16 | Issue:2 Page(s): 1-10

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Information Journal Paper

Title

Determination of Gain and Phase Margins in Lur’e Nonlinear Systems using Extended Circle Criterion

Author(s)

Delavar Abolfazl | Haeri Mohammad | Issue Writer Certificate

Keywords

Stability marginsQ4

Stability of Lur’e type systemsQ4

Practical gain and phase marginsQ4

Extended circle criterionQ4

Bilinear matrix inequalityQ4

Abstract

Nonlinearity is one of the main behaviors of systems in the real world. Therefore, it seems necessary to introduce a method to determine the stability margin of these systems. Although the gain and phase margins are established criteria for the analysis of linear systems, finding a specific way to determine the true value of these margins in nonlinear systems in general is an ongoing research in the literature. The main goal of this paper is to introduce a new method to determine these margins more precisely for particular type of nonlinearities. Based on Lyapunov theorem, stability conditions are obtained and the Stability margins of Lur'e systems are determined by applying the Extended circle criterion. By providing numerical examples, the correctness of the obtained results is checked and by comparing them with other methods, the accuracy of the obtained results is evaluated.

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