Abstract
The problem of designing a digital controller stabilizing a continuous-time switched linear control delay system is studied. The approach to stabilization successively includes the construction of a continuous-time–discrete-time closed-loop system with a digital controller, the transition to its discrete-time model, and the construction of a discrete-time controller by 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
Fursov, A.S., Minyaev, S.I., and Iskhakov, E.A., Digital stabilizer design for a switched linear system, Differ. Equations, 2017, vol. 53, no. 8, pp. 1093–1099.
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.
Hespanha, J.P., Uniform stability of switched linear systems: extensions of LaSalle’s invariance principle, IEEE Trans. Autom. Control, 2004, vol. 49, no. 4, pp. 470–482.
Vasil’ev, S.N. and Malikov, A.I., Some results on stability of switched and hybrid systems, in Aktual’nye problemy mekhaniki sploshnykh sred (Topical Problems of Continuum Mechanics), Dedicated to the 20th Anniversary of IMM KazNTs, Kazan, 2011, vol. 1, pp. 23–81.
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 (survey), Avtometriya, 2008, vol. 44, no. 5, pp. 71–87.
Sun, Z. and Ge, S.S., Stability Theory of Switched Dynamical Systems, London: Springer, 2011.
Liberzon, D., Switching in Systems and Control, Basel: Dekker, 2003.
Mahmoud, M.S., Switched Time-Delay Systems. Stability and Control, New York–London: Springer, 2010.
Chen, T. and Francis, B., Optimal Sampled-Data Control Systems, Berlin: Springer, 1994.
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.
Jaulin, L., Kieffer, M., Didrit, O., and Walter, E., Applied Interval Analysis, London: Springer, 2001. Translated under the title Prikladnoi interval’nyi analiz, Moscow–Izhevsk: Inst. Komp. Issled., 2007.
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, V.S. Guseva, 2018, published in Differentsial’nye Uravneniya, 2018, Vol. 54, No. 8, pp. 1132–1141.
Rights and permissions
About this article
Cite this article
Fursov, A.S., Minyaev, S.I. & Guseva, V.S. Digital Stabilizer Design for a Switched Linear Control Delay System. Diff Equat 54, 1115–1124 (2018). https://doi.org/10.1134/S0012266118080104
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0012266118080104