Mathematics

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Research from the Department of Mathematics. The department website may be found at https://www.ndsu.edu/math/

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Browsing Mathematics by Subject "Control theory."

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    Absolute Stability of a Class of Second Order Feedback Non-Linear, Time-Varying Systems
    (North Dakota State University, 2010) Omotoyinbo, Tayo
    In this thesis, we consider the problem of absolute stability of continuous time feedback systems with a single, time-varying nonlinearity. Necessary and sufficient conditions for absolute stability of second-order systems in terms of system parameters are developed, which are characterized by eigenvalue locations on the complex plane. More specifically, our results are presented in terms of the associated matrix-pencil {A+ bvc*, v E [11,1, /L2]}, where /Li, /J,2 E ffi., A is n x n-matrix, b and c are n-vectors. The stability conditions require that the eigenvalues of all matrices A +bvc*, p1 ~ v ~ μ2, lie in the interior of a specific region of the complex plane ( a cone to be specific). Thus, we have the following reformulation of the problem. Find the maximal cone satisfying the following condition: If all eigenvalues of corresponding linear systems belong to this cone, then system is absolutely stable. Known results show that this cone is not smaller than { z E