Abstract
In this paper, the finite-time control problem for Markov systems with partly known transition probabilities and polytopic uncertainties is investigated. The main result provided is a sufficient conditions for finite-time stabilization via state feedback controller, and a simpler case without controller is also considered, based on switched quadratic Lyapunov function approach. All conditions are shown in the form of LMIs. An illustrative example is presented to demonstrate the result.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
References
Zhang, L., Boukas, E.K., Lam, J.: Analysis and synthesis of Markov jump linear systems with time-varying delays and partially known transition probabilities. IEEE Trans. Auto. Con. 53, 2458–2464 (2008)
Zhang, L., Boukas, E.K., Baron, L.: Fault detection for discrete-time Markov jump linear systems with partially known transition probabilities. Int. J. Con. 83, 1564–1572 (2010)
Braga, M.F., Morais, C.F., Oliveira, R.C.L.F.: Robust stability and stabilization of discrete-time Markov jump linear systems with partly unknown transition probability matrix. In: American Control Conference (ACC), pp. 6784–6789. IEEE Press, Washington (2013)
Tian, E., Yue, D., Wei, G.: Robust control for Markovian jump systems with partially known transition probabilities and nonlinearities. J. Fran. Ins. 350, 2069–2083 (2013)
Shen, M., Yang, G.H.: H 2 state feedback controller design for continuous Markov jump linear systems with partly known information. Inter. J. Sys. Sci. 43, 786–796 (2012)
Tian, J., Li, Y., Zhao, J.: Delay-dependent stochastic stability criteria for Markovian jumping neural networks with mode-dependent time-varying delays and partially known transition rates. Ap. Mathe. Com. 218, 5769–5781 (2012)
Rao, R., Zhong, S., Wang, X.: Delay-dependent exponential stability for Markovian jumping stochastic Cohen-Grossberg neural networks with p-Laplace diffusion and partially known transition rates via a differential inequality. Ad. Differ. Equa. 2013, 1–14 (2013)
Amato, F., Ariola, M., Dorato, P.: Finite-time control of linear systems subject to parametric uncertainties and disturbances. Auto. 37, 1459–1463 (2001)
Zhang, X., Feng, G., Sun, Y.: Finite-time stabilization by state feedback control for a class of time-varying nonlinear systems. Auto. 48, 499–504 (2012)
Hu, M., Cao, J., Hu, A.: A Novel Finite-Time Stability Criterion for Linear Discrete-Time Stochastic System with Applications to Consensus of Multi-Agent System. Cir. Sys. Sig. Pro. 34, 1–19 (2014)
Zhou, J., Xu, S., Shen, H.: Finite-time robust stochastic stability of uncertain stochastic delayed reaction-diffusion genetic regulatory networks. Neu. 74, 2790–2796 (2011)
Zuo, Z., Li, H., Wang, Y.: Finite-time stochastic stabilization for uncertain Markov jump systems subject to input constraint. Trans. Ins. Mea. Con. 36, 283–288 (2014)
Yin, Y., Liu, F., Shi, P.: Finite-time gain-scheduled control on stochastic bioreactor systems with partially known transition jump rates. Cir. Sys. Sig. Pro. 30, 609–627 (2011)
Bhat, S.P., Bernstein, D.S.: Continuous finite-time stabilization of the translational and rotational double integrators. IEEE Trans. Auto. Con. 43, 678–682 (1998)
Luan, X., Liu, F., Shi, P.: Neural-network-based finite-time H ∞ control for extended Markov jump nonlinear systems. Inter. J. Adap. Con. Sig. Pro. 24, 554–567 (2010)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Zheng, C., Fan, X., Hu, M., Yang, Y., Jin, Y. (2015). Finite-Time Control for Markov Jump Systems with Partly Known Transition Probabilities and Time-Varying Polytopic Uncertainties. In: Hu, X., Xia, Y., Zhang, Y., Zhao, D. (eds) Advances in Neural Networks – ISNN 2015. ISNN 2015. Lecture Notes in Computer Science(), vol 9377. Springer, Cham. https://doi.org/10.1007/978-3-319-25393-0_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-25393-0_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-25392-3
Online ISBN: 978-3-319-25393-0
eBook Packages: Computer ScienceComputer Science (R0)