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Network-based control of discrete-time descriptor systems with random delays. (English) Zbl 1228.93076
Summary: This paper addresses the network-based control problem for a class of descriptor systems in the discrete-time domain with random delays. By modeling the sensor-to-controller and controller-to-actuator delays as Markovian chains, the closed-loop system can be expressed as a jump linear descriptor system with two modes. The stochastically admissible necessary and sufficient condition for the closed-loop system is constructed. An explicit expression for the desired controller is given without any system decomposition. The obtained results are formulated in terms of strict Linear Matrix Inequalities (LMIs). In addition, an example is given to illustrate the effectiveness of the proposed approach.
MSC:
93C55Discrete-time control systems
60J10Markov chains (discrete-time Markov processes on discrete state spaces)
93E03General theory of stochastic systems
References:
[1]L. Dai, Singular Control Systems (Springer, Berlin, 1989)
[2]J.P. Hespanha, P. Naghshtabrizi, Y.G. Xu, A survey of recent results in networked control systems. Proc. IEEE 95, 138–162 (2007) · doi:10.1109/JPROC.2006.887288
[3]J. Lam, Z. Shu, S.Y. Xu, E.K. Boukas, Robust H control of descriptor discrete-time Markovian jump systems. Int. J. Control 80(3), 374–385 (2007) · Zbl 1120.93057 · doi:10.1080/00207170600999322
[4]G.P. Lu, Z.P. Jiang, State estimation for networked descriptor systems with limited information, in Proc. 25th Chinese Control Conference, Harbin (2006), pp. 1796–1801
[5]G.P. Lu, G. Feng, Z.P. Jiang, Saturated feedback stabilization of discrete-time descriptor bilinear systems. IEEE Trans. Autom. Control 52(9), 1700–1704 (2007) · doi:10.1109/TAC.2007.904282
[6]L.A. Montestruque, Stability of model-based networked control systems with time-varying transmission times. IEEE Trans. Autom. Control 49(9), 1562–1572 (2004) · doi:10.1109/TAC.2004.834107
[7]Z.Z. Qiu, Q.L. Zhang, C.H. Diao, L. Yang, Robust stability of a class of networked control systems based on descriptor system, in Proc. 1st International Symposium on Systems and Control in Aerospace and Astronautics (2006), pp. 1166–1170
[8]Y. Shi, B. Yu, Output feedback stabilization of networked control systems with random delays modeled by Markov chains. IEEE Trans. Autom. Control 54, 1668–1674 (2009) · doi:10.1109/TAC.2009.2020638
[9]Y.Q. Xia, J.H. Zhang, E.K. Boukas, Control for discrete singular hybrid systems. Automatica 44(10), 2635–2641 (2008) · Zbl 1155.93359 · doi:10.1016/j.automatica.2008.02.027
[10]L. Xiao, H. Arash, P. Jonathan, Control with random communication delays via a discrete time jump system approach, in Proc. American Control Conference, Chicago, IL, USA, June (2000), pp. 2199–2204
[11]S.Y. Xu, J. Lam, Robust Control and Filtering of Singular Systems (Springer, Berlin, 2006)
[12]M. Yu, L. Wang, T. Chu, F. Hao, An LMI approach to networked control systems with data packet dropout and transmission delays, in Proc. 43rd IEEE Conf. Decision and Control (2004), pp. 3545–3550
[13]D. Yue, Q.L. Han, P. Chen, State feedback controller design of networked control systems. IEEE Trans. Circuits Syst. II, Express Briefs 51(11), 640–644 (2004) · doi:10.1109/TCSII.2004.836043
[14]L.Q. Zhang, Y. Shi, T.W. Chen, B. Huang, A new method for stabilization of networked control systems with random delays. IEEE Trans. Autom. Control 50(8), 1177–1181 (2005) · doi:10.1109/TAC.2005.852550
[15]W. Zhang, M.S. Braniky, S.M. Phillips, Stability of networked control systems. IEEE Control Syst. Mag. 21, 84–89 (2001) · doi:10.1109/37.898794