Abstract
We consider the problem of constructing a common controller stabilizing a finite family of linear dynamic plants of various orders with respect to state. For the solution, we use the method of extension of dynamic order, which permits one to reduce the original problem to a problem of simultaneous stabilization of plants of the same order. We state conditions for the existence of a universal stabilizer for a given finite family of dynamic plants.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Birdwell, J., Castanon, D., and Athans, M., On Reliable Control Systems Designs with and without Feedback Reconfiguration, Proc. IEEE Conf. on Dec. and Control, San Diego, 1979, pp. 419–426.
Saeks, R. and Murray, J., Fractional Representations, Algebraic Geometry and the Simultaneous Stabilization Problem, IEEE Trans. Automat. Control, AC-27, 1982, pp. 895–903.
Blondel, V., Simultaneous Stabilization of Linear Systems, London, 1994.
Korovin, S.K., Kudritskii, A.V., and Fursov, A.S., On the Simultaneous Stabilization of Linear Plants of Arbitrary Order by a Controller with a Given Structure, Dokl. Akad. Nauk, 2008, vol. 423, no. 2, pp. 173–177.
Korovin, S.K., Kudritskii, A.V., and Fursov, A.S., On the Simultaneous α-Stabilization of Linear Plants, Differ. Uravn., 2009, vol. 45, no. 5, pp. 698–705.
Korovin, S.K., Il’in, A.V., Fomichev, V.V., and Fursov, A.S., A Topological Approach to the Problem of the Existence of a Common Stabilizer for a Family of Dynamical Systems, Dokl. Akad. Nauk, 2011, vol. 441, no. 6, pp. 737–742.
Emel’yanov, S.V., Fomichev, V.V., and Fursov, A.S., Simultaneous Stabilization of Linear Dynamic Plants by a Regulator of a Variable Structure, Avtomat. i Telemekh., 2012, no. 7, pp. 15–24.
Emel’yanov, S.V., Systems of Automated Controls of Variable Structure: Synthesis of Scalar and Vector Systems with Respect to State and Output, in Nelineinaya dinamika i upravlenie: Sb. statei (Nonlinear Dynamics and Control. Collection of Works), Emel’yanov, S.V. and Korovin, S.K., Eds., Moscow, 2006.
Filippov, A.F., Differentsial’nye uravneniya s razryvnoi pravoi chast’yu (Differential Equations with a Discontinuous Right-Hand Side), Moscow, 1985.
Kim, D.P., Teoriya avtomaticheskogo upravleniya (Theory of Automated Control), Moscow, 2004, vol. 2.
Balandin, D.V. and Kogan, M.M., Sintez zakonov upravleniya na osnove lineinykh matrichnykh neravenstv (Synthesis of Control Laws on the Basis of Linear Matrix Inequalities), Moscow, 2007.
Polyak, B.T. and Shcherbakov, P.S., Robastnaya ustoichivost’ i upravlenie (Robust Stability and Control), Moscow, 2002.
Author information
Authors and Affiliations
Additional information
Dedicated to the glorious jubilee of Academician V.A. Il’in
Original Russian Text © S.V. Emel’yanov, A.V. Il’in, V.V. Fomichev, A.S. Fursov, 2013, published in Differentsial’nye Uravneniya, 2013, Vol. 49, No. 5, pp. 649–655.
Rights and permissions
About this article
Cite this article
Emel’yanov, S.V., Il’in, A.V., Fomichev, V.V. et al. Simultaneous stabilization of plants of various orders. Diff Equat 49, 623–629 (2013). https://doi.org/10.1134/S001226611305011X
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S001226611305011X