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On stabilization of differential systems with hybrid feedback control


In this paper two-dimensional systems of differential equations are considered together with their stabilization by a hybrid feedback control. A stabilizing hybrid control for an arbitrary controlled system that belongs to a certain category within two-dimensional systems is constructed as a result of this study and some stabilization proprieties of the system with the obtained hybrid control are presented.


stabilization; hybrid feedback control; linear hybrid control; upper Lyapunov Exponent

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1. Litsyn E., Nepomnyashchikh Y., Ponossov A. Classification of linear dynamical systems in the plane admitting a stabilizing hybrid feedback control. Journal on Dynamical and Control Systems, 2000, vol. 6, no. 4, pp. 477-501. 2. Litsyn E., Myasnikova M., Nepomnyashchikh Y., Ponossov A. Efficient criteria for stabilization of planar linear systems by hybrid feedback controls. Abstract and Applied Analysis, 2004, no. 6, pp. 487-499. 3. Litsyn E., Nepomnyashchikh Y., Ponossov A. Control of the Lyapunov exponents of dynamical systems in the plane with incomplete observation. Nonlinear Analysis. Series A: Theory, Methods & Applications, Special issue: Hybrid Systems and Applications, 2005, vol. 64, no. 2, pp. 329-351. 4. Alves M.J. Singulyarnye funktsional’no-differentsial’nye uravneniya vtorogo poryadka [Singular Second Order Functional Differential Equations]. Perm, Perm State University Publ., 2000, 179 p. (In Russian). 5. Korotaeva I.G. Ehksponentsial’naya stabilizatsiya dvumernykh gibridnykh system [Exponential Stabilization of Two-Dimensional Linear Hybrid Systems]. Perm, 2003, 35 p. (In Russian). 6. Myasnikova M.A. Klassifikatsiya lineynykh dvumernykh gibridnykh system [Classification of Two-Dimensional Linear Hybrid Systems]. Perm, 2003, 51 p. (In Russian). 7. Lay D.C. Linear Algebra and Its Applications. Boston, Pearson Education Inc., 2012, 472 p.



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