×
Xiong, Junlin; Lam, James

Stabilization of discrete-time Markovian jump linear systems via time-delayed controllers. (English) Zbl 1137.93421

Automatica 42, No. 5, 747-753 (2006).
Summary: This paper is concerned with the stabilization problem for a class of discrete-time Markovian jump linear systems with time-delays both in the system state and in the mode signal. The delay in the system state may be time-varying. The delay in the mode signal is manifested as a constant mismatch of the modes between the controller and the system. We first show that the resulting closed-loop system is a time-varying delayed Markovian jump linear system with extended state space. Then a sufficient condition is proposed for the design of a controller such that the closed-loop system is stochastically stable. Finally, numerical simulation is used to illustrate the developed theory.

Cited in 75 Documents

MSC:

93E15 Stochastic stability in control theory
93E20 Optimal stochastic control
93C55 Discrete-time control/observation systems
60J05 Discrete-time Markov processes on general state spaces

Keywords:

linear matrix inequalities; Markovian parameters; stabilization; time-delay
PDF BibTeX XML Cite
\textit{J. Xiong} and \textit{J. Lam}, Automatica 42, No. 5, 747--753 (2006; Zbl 1137.93421)
Full Text: DOI
  • logo of hbz
  • logo of WorldCat

References:

[1] Abou-Kandil, H.; Freiling, G.; Jank, G., On the solution of discrete-time Markovian jump linear quadratic control problems, Automatica, 31, 5, 765-768, (1995) · Zbl 0822.93074
[2] Boukas, E.K.; Liu, Z.K., Robust \(H_\infty\) control of discrete-time Markovian jump linear systems with mode-dependent time-delays, IEEE transactions on automatic control, 46, 12, 1918-1924, (2001) · Zbl 1005.93050
[3] Cao, Y.-Y.; Lam, J., Stochastic stabilizability and \(H_\infty\) control for discrete-time jump linear systems with time delay, Journal of the franklin institute, 336, 8, 1263-1281, (1999) · Zbl 0967.93095
[4] 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, Systems and control letters, 52, 5, 361-376, (2004) · Zbl 1157.93438
[5] Costa, O.L.V., Stability results for discrete-time linear systems with Markovian jumping parameters, Journal of mathematical analysis and applications, 179, 1, 154-178, (1993) · Zbl 0790.93108
[6] Costa, O.L.V.; Fragoso, M.D.; Marques, R.P., Discrete-time Markov jump linear systems, (2005), Springer London · Zbl 1081.93001
[7] Costa, O.L.V.; Guerra, S., Robust linear filtering for discrete-time hybrid Markov linear systems, International journal of control, 75, 10, 712-727, (2002) · Zbl 1018.93028
[8] Costa, O.L.V.; Marques, R.P., Mixed \(H_2 / H_\infty\)-control of discrete-time Markovian jump linear systems, IEEE transactions on automatic control, 43, 1, 95-100, (1998) · Zbl 0907.93062
[9] Ghaoui, L.E.; Oustry, F.; Rami, M.A., A cone complementarity linearization algorithm for static output-feedback and related problems, IEEE transactions on automatic control, 42, 8, 1171-1176, (1997) · Zbl 0887.93017
[10] Ji, Y.; Chizeck, H.J., Jump linear quadratic Gaussian control: steady-state solution and testable conditions, Control theory and advanced technology, 6, 3, 289-319, (1990)
[11] Ji, Y.; Chizeck, H.J.; Feng, X.; Loparo, K.A., Stability and control of discrete-time jump linear systems, Control theory and advanced technology, 7, 2, 247-270, (1991)
[12] Leibfritz, F., An LMI-based algorithm for designing suboptimal static \(H_2 / H_\infty\) output feedback controllers, SIAM journal on control and optimization, 39, 6, 1711-1735, (2001) · Zbl 0997.93032
[13] Liu, H.; Sun, F.; Sun, Z., Reduced-order filtering with energy-to-peak performance for discrete-time Markovian jumping systems, IMA journal of mathematical control and information, 21, 2, 143-158, (2004) · Zbl 1067.93058
[14] Richard, J.-P., Time-delay systems: an overview of some recent advances and open problems, Automatica, 39, 10, 1667-1694, (2003) · Zbl 1145.93302
[15] Seiler, P.; Sengupta, R., A bounded real lemma for jump systems, IEEE transactions on automatic control, 48, 9, 1651-1654, (2003) · Zbl 1364.93223
[16] Shi, P.; Boukas, E.-K.; Agarwal, R.K., Control of Markovian jump discrete-time systems with norm bounded uncertainty and unknown delay, IEEE transactions on automatic control, 44, 11, 2139-2144, (1999) · Zbl 1078.93575
[17] Xiong, J.; Lam, J.; Gao, H.; Ho, D.W.C., On robust stabilization of Markovian jump systems with uncertain switching probabilities, Automatica, 41, 5, 897-903, (2005) · Zbl 1093.93026
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.