Top

Published in:

2018 | OriginalPaper | Chapter

2. Robust Stochastic Stability

Authors : Yu Kang, Yun-Bo Zhao, Ping Zhao

Published in: Stability Analysis of Markovian Jump Systems

Publisher: Springer Singapore

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

This chapter investigates the robust output feedback \(H_{\infty }\) control for a class of uncertain Markovian jump linear systems with mode-dependent time-varying time delays. With known bounds of the system uncertainties and the control gain variations, we develop the sufficient conditions to guarantee the robust stochastic stability and the \(\gamma \)-disturbance \(H_{\infty }\) attenuation for the closed-loop system.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

previous chapter Introduction to Markovian Jump Systems

next chapter System with Imprecise Jumping Parameters

Benjelloun, K., Boukas, E.K.: Independent delay sufficient conditions for robust stability of uncertain linear time-delay systems with jumps. In: Proceedings of the 1997 American Control Conference, vol. 6, pp. 3814–3815. Albuquerque, NM (1997)

Benjelloun, K., Boukas, E.K., Costa, O.L.V.: \(H_{\infty }\) control for linear time-delay systems with Markovian jumping parameters. In: Proceedings of the 38th IEEE Conference on Decision and Control, vol. 2, pp. 1567–1572 (1999)

Boukas, E.K., Liu, Z.K.: Output-feedback guaranteed cost control for uncertain time-delay systems with Markov jumps. In: Proceedings of the 2000 American Control Conference, vol. 4, pp. 2784–2788. Chicago, IL (2000)

Boukas, E.K., Liu, Z.K.: Output feedback robust stabilization of jump linear system with mode-dependent time-delays. In: Proceedings of the 2001 American Control Conference, vol. 6, pp. 4683–4688. Arlington, VA (2001)

Boukas, E.K., Liu, Z.K.: Deterministic and Stochastic Time Delay Systems. Springer, Berlin (2002)CrossRefMATH

Caines, P.E., Zhang, J.F.: On the adaptive control for jump parameter system via nonlinear filtering. SIAM J. control. Optim. 33(6), 1758–1777 (1995)MathSciNetCrossRefMATH

Cao, Y.Y., James, L.: Robust \(H_{\infty }\) control of uncertain Markovian jump systems with time-delay. IEEE Trans. Autom. Control. 45(1), 77–83 (2000)MathSciNetCrossRefMATH

Chen, W.H., Guan, Z.H., Yu, P.: Delay-dependent stability and \({H}_\infty \) control of uncertain discrete-time Markovian jump systems with mode-dependent time delays. Syst. Control Lett. 52(5), 361–376 (2004)MathSciNetCrossRefMATH

Chen, W.H., Xu, J.X., Guan, Z.H.: Guaranteed cost control for uncertain Markovian jump systems with mode-dependent time-delays. IEEE Trans. Autom. Control. 48(12), 2270–2277 (2003)MathSciNetCrossRefMATH

10.

Esfahani, S.H., Petersen, I.R.: An LMI approach to output-feedback-guaranteed cost control for uncertain time-delay systems. Int. J. Robust Nonlinear Control. 10(3), 157–174 (2000)MathSciNetCrossRefMATH

11.

Fridman, E., Shaked, U.: An improved stabilization method for linear time-delay systems. IEEE Trans. Autom. Control. 47(11), 1931–1937 (2002)MathSciNetCrossRefMATH

12.

Fridman, E., Shaked, U.: Delay-dependent stability and \({H}_\infty \) control: constant and time-varying delays. Int. J. Control. 76(1), 48–60 (2003)MathSciNetCrossRefMATH

13.

Gahinet, P.: Explicit controller formulas for LMI-based \({H}_\infty \) synthesis. Automatica 32(7), 1007–1014 (1996)MathSciNetCrossRefMATH

14.

Ge, S., Hong, F., Lee, T.: Adaptive neural control of nonlinear time-delay systems with unknown virtual control coefficients. IEEE Trans. Syst. Man Cybern. Part B: Cybern. 38(1), 671–682 (2002)

15.

Ge, S., Hong, F., Lee, T.: Robust adaptive control of nonlinear systems with unknown time delays. Automatica 41(7), 1181–1190 (2005)MathSciNetCrossRefMATH

16.

Hale, J.: Theory of Functional Differential Equations, 2nd edn. Springer, Berlin (1977)CrossRefMATH

17.

Kreindler, E., Jameson, A.: Conditions for nonnegativeness of partitioned matrices. IEEE Trans. Autom. Control. 17(1), 147–148 (1972)MathSciNetCrossRefMATH

18.

Kushner, H.J.: Stochastic Stability and Control. Academic Press, New York (1967)MATH

19.

Mariton, M.: Jump Linear Systems in Automatic Control. Marcel Dekker, New York (1990)

20.

Mariton, M.: Control of nonlinear systems with Markovian parameter changes. IEEE Trans. Autom. Control. 36(2), 233–238 (1991)MathSciNetCrossRefMATH

21.

Masubuchi, I., Ohara, A., Suda, N.: LMI-based controller synthesis: A unified formulation and solution. Int. J. Robust Nonlinear Control. 8(8), 669–686 (1998)MathSciNetCrossRefMATH

22.

Moon, Y.S., Park, P., Kwon, W.H.: Delay-dependent robust stabilization of uncertain state-delayed systems. Int. J. Control. 74(14), 1447–1455 (2001)MathSciNetCrossRefMATH

23.

Park, P.: A delay-dependent stability criterion for systems with uncertain time-invariant delays. IEEE Trans. Autom. Control. 44(4), 876–877 (1999)MathSciNetCrossRefMATH

24.

Wu, M., He, Y., She, J., Liu, G.: Delay-dependent criteria for stability of time-varying delay systems. Automatica 40(8), 1435–1439 (2004)MathSciNetCrossRefMATH

25.

Xie, L.: Output feedback \(H_{\infty }\) control of systems with parameter uncertainty. Int. J. Control. 63(4), 741–750 (1996)MathSciNetCrossRefMATH

26.

Xu, S., Chen, T.: H\(_\infty \) output feedback control for uncertain stochastic systems with time-varying delays. Automatica 40(12), 2091–2098 (2004)MathSciNetMATH

27.

Xu, S., Chen, T.W., Lam, J.: Robust \(H_{\infty }\) filtering for uncertain Markovian jump systems with mode-dependent time delays. IEEE Trans. Autom. Control 48(5), 900–907 (2003)CrossRefMATH

Title: Robust Stochastic Stability
Authors: Yu Kang
Yun-Bo Zhao
Ping Zhao
Publisher: Springer Singapore
Book: Stability Analysis of Markovian Jump Systems
Print ISBN: 978-981-10-3859-4

Electronic ISBN: 978-981-10-3860-0

Copyright Year: 2018
DOI: https://doi.org/10.1007/978-981-10-3860-0_2