Abstract
We consider the problem of designing a digital controller stabilizing a continuoustime switched linear system. Our approach to stabilization includes the construction of a continuous-discrete time closed-loop system, the passage to its discrete-time model, and the subsequent discrete-time controller design based on simultaneous stabilization methods.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Hespanha, J.P., Uniform stability of switched linear systems: extensions of LaSalle’s invariance principle, IEEE Trans. Autom. Control, 2014, vol. 49, no. 4, pp. 470–482.
Emel’yanov, S.V., Sistemy avtomaticheskogo upravleniya s peremennoi strukturoi (Automatic Control Systems of Variable Structure), Moscow: Nauka, 1967.
Kim, D.P., Teoriya avtomaticheskogo upravleniya, vol. 2: Mnogomernye, nelineinye, optimal’nye i adaptivnye sistemy (Automatic Control Theory, vol. 2: Multidimensional, Nonlinear, Optimal, and Adaptive Systems), Moscow: Fizmatlit, 2004.
Polyak, B.T. and Shcherbakov, P.S., Robastnaya ustoichivost’ i upravlenie (Robust Stability and Control), Moscow: Nauka, 2002.
Aleksandrov, A.G., Optimal’nye i adaptivnye sistemy (Optimal and Adaptive Systems), Moscow: Vysshaya Shkola, 1989.
Liberzon, D. and Morse, A.S., Basic problems in stability and design of switched systems, IEEE Control Syst., 1999, vol. 19, no. 5, pp. 59–70.
Shpilevaya, O.A. and Kotov, K.Yu., Switched systems: stability and design (a survey), Avtometriya, 2008, vol. 44, no. 5, pp. 71–87.
Fursov, A.S. and Khusainov, E.F., On the stabilization of switchable linear systems, Differ. Equations, 2015, vol. 51, no. 11, pp. 1518–1528.
Fursov, A.S. and Kapalin, I.V., Stabilization of switched linear systems by a controller of variable structure, Differ. Equations, 2016, vol. 52, no. 8, pp. 1072–1084.
Korovin, S.K., Minyaev, S.I., and Fursov, A.S., Approach to simultaneous stabilization of linear dynamic plants with delay, Differ. Equations, 2011, vol. 47, no. 11, pp. 1612–1618.
Chen, T. and Francis, B., Optimal Sample-Data Control Systems, Berlin: Springer-Verlag, 1994.
Polyakov, K.Yu., Osnovy teorii tsifrovykh sistem upravleniya (Foundations of the Theory of Digital Control Systems), St. Petersburg: St. Peterb. Gos. Morsk. Tekh. Univ., 2002.
Fursov, A.S., Odnovremennaya stabilizatsiya: teoriya postroeniya universal’nogo regulyatora dlya semeistva dinamicheskikh ob”ektov (Simultaneous Stabilization: Design Theory of a Universal Controller for a Family of Dynamic Plants), Moscow: Argamak-Media, 2016.
Emel’yanov, S.V., Korovin, S.K., Il’in, A.V., Fomichev, V.V., and Fursov, A.S., Matematicheskie metody teorii upravleniya. Problemy ustoichivosti, upravlyaemosti i nablyudaemosti (Mathematical Methods of Control Theory: Stability, Controllability, and Observability Problems), Moscow: Fizmatlit, 2013.
Polyak, B.T., Khlebnikov, M.V., and Shcherbakov, P.S., Upravlenie sistemami pri vneshnikh vozmushcheniyakh: Tekhnika lineinykh matrichnykh neravenstv (Control of Systems under External Disturbances: Linear Matrix Inequality Technique), Moscow: URSS, 2014.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A.S. Fursov, S.I. Minyaev, E.A. Iskhakov, 2017, published in Differentsial’nye Uravneniya, 2017, Vol. 53, No. 8, pp. 1121–1127.
Rights and permissions
About this article
Cite this article
Fursov, A.S., Minyaev, S.I. & Iskhakov, E.A. Digital stabilizer design for a switched linear system. Diff Equat 53, 1093–1099 (2017). https://doi.org/10.1134/S0012266117080146
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0012266117080146