A new delay system approach to network-based control.

*(English)*Zbl 1138.93375Summary: This paper presents a new delay system approach to network-based control. This approach is based on a new time-delay model proposed recently, which contains multiple successive delay components in the state. Firstly, new results on stability and \(\mathcal H _{\infty}\) performance are proposed for systems with two successive delay components, by exploiting a new Lyapunov-Krasovskii functional and by making use of novel techniques for time-delay systems. An illustrative example is provided to show the advantage of these results. The second part of this paper utilizes the new model to investigate the problem of network-based control, which has emerged as a topic of significant interest in the control community. A sampled-data networked control system with simultaneous consideration of network induced delays, data packet dropouts and measurement quantization is modeled as a nonlinear time-delay system with two successive delay components in the state and, the problem of network-based \(\mathcal H _{\infty}\) control is solved accordingly. Illustrative examples are provided to show the advantage and applicability of the developed results for network-based controller design.

##### MSC:

93C57 | Sampled-data control/observation systems |

93B35 | Sensitivity (robustness) |

93D20 | Asymptotic stability in control theory |

93C05 | Linear systems in control theory |

##### Keywords:

linear matrix inequality (LMI); networked control systems (NCSs); sampled-data systems; stability; time-delay systems
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##### References:

[1] | Antsaklis, P.; Baillieul, J., Guest editorial special issue on networked control systems, IEEE transactions on automatic control, 31, 9, 1421-1423, (2004) · Zbl 1365.93005 |

[2] | Biernacki, R.M.; Hwang, H.; Battacharyya, S.P., Robust stability with structured real parameter perturbations, IEEE transactions on automatic control, 32, 495-506, (1987) |

[3] | El Ghaoui, L.; 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 |

[4] | Elia, N.; Mitter, S.K., Stabilization of linear systems with limited information, IEEE transactions on automatic control, 46, 9, 1384-1400, (2001) · Zbl 1059.93521 |

[5] | Fridman, E.; Shaked, U., Delay-dependent stability and \(H_\infty\) control: constant and time-varying delays, International journal of control, 76, 1, 48-60, (2003) · Zbl 1023.93032 |

[6] | Fu, M.; Xie, L., The sector bound approach to quantized feedback control, IEEE transactions on automatic control, 50, 11, 1698-1711, (2005) · Zbl 1365.81064 |

[7] | Gao, H.; Lam, J.; Wang, C.; Xu, S., \(H_\infty\) model reduction for discrete time-delay systems: delay independent and dependent approaches, International journal of control, 77, 321-335, (2004) · Zbl 1066.93009 |

[8] | Gao, H.; Wang, C., Comments and further results on A descriptor system approach to \(H_\infty\) control of linear time-delay systems, IEEE transactions on automatic control, 48, 3, 520-525, (2003) · Zbl 1364.93211 |

[9] | Gao, H.; Wang, C., A delay-dependent approach to robust \(H_\infty\) filtering for uncertain discrete-time state-delayed systems, IEEE transactions of signal processing, 52, 6, 1631-1640, (2004) · Zbl 1369.93175 |

[10] | Goodwin, G.C.; Haimovich, H.; Quevedo, D.E.; Welsh, J.S., A moving horizon approach to networked control system design, IEEE transactions on automatic control, 49, 9, 1427-1445, (2004) · Zbl 1365.93172 |

[11] | Gu, K.; Kharitonov, V.L.; Chen, J., Stability of time-delay systems, (2003), Springer Berlin · Zbl 1039.34067 |

[12] | Hale, J.; Lunel, S.M.V., Introduction to functional differential equations, (1993), Springer Berlin |

[13] | He, Y.; Wang, Q.-G.; Lin, C.; Wu, M., Delay-range-dependent stability for systems with time-varying delay, Automatica, 43, 2, 371-376, (2007) · Zbl 1111.93073 |

[14] | He, Y.; Wang, Q.G.; Xie, L.H.; Lin, C., Further improvement of free-weighting matrices technique for systems with time-varying delay, IEEE transactions on automatic control, 52, 2, 293-299, (2007) · Zbl 1366.34097 |

[15] | He, Y.; Wu, M.; She, J.H.; Liu, G.P., Parameter-dependent Lyapunov functional for stability of time-delay systems with polytopic-type uncertainties, IEEE transactions on automatic control, 49, 5, 828-832, (2004) · Zbl 1365.93368 |

[16] | Hua, C.; Guan, X.; Shi, P., Robust backstepping control for a class of time delayed systems, IEEE transactions on automatic control, 50, 6, 894-899, (2005) · Zbl 1365.93054 |

[17] | Ishii, H., & Francis, B. A. (2002). Limited data rate in control systems with networks (vol. 275), Lecture Notes in Control and Information Sciences. Berlin: Springer. · Zbl 1001.93001 |

[18] | Jing, X.J.; Tan, D.L.; Wang, Y.C., An LMI approach to stability of systems with severe time-delay, IEEE transactions on automatic control, 49, 7, 1192-1195, (2004) · Zbl 1365.93226 |

[19] | Kim, J.-H., Delay and its time-derivative dependent robust stability of time-delayed linear systems with uncertainty, IEEE transactions on automatic control, 46, 5, 789-792, (2001) · Zbl 1008.93056 |

[20] | Lam, J.; Gao, H.; Wang, C., Stability analysis for continuous systems with two additive time-varying delay components, Systems control letters, 56, 1, 16-24, (2007) · Zbl 1120.93362 |

[21] | Lee, Y. S., Moon, Y. S., Kwon, W. H., & Lee, K. H. (2001). Delay-dependent robust \(H_\infty\) control for uncertain systems with time-varying state-delay. In Proceedings of the 40th conference on decision control (pp. 3208-3213), Orlando, FL. |

[22] | Lian, F.-L.; Moyne, J.; Tilbury, D., Modelling and optimal controller design of networked control systems with multiple delays, International journal of control, 76, 6, 591-606, (2003) · Zbl 1050.93038 |

[23] | Lin, C.; Wang, Q.-G.; Lee, T.H., A less conservative robust stability test for linear uncertain time-delay systems, IEEE transactions on automatic control, 51, 1, 87-91, (2006) · Zbl 1366.93469 |

[24] | Liu, H.; Sun, F.; He, K.; Sun, Z., Design of reduced-order \(H_\infty\) filter for Markovian jumping systems with time delay, IEEE transactions on circuits and systems (II), 51, 607-612, (2004) |

[25] | Montestruque, L.A.; Antsaklis, P., Stability of model-based networked control systems with time-varying transmission times, IEEE transaction on automatic control, 49, 9, 1562-1572, (2004) · Zbl 1365.90039 |

[26] | Niculescu, S.I., Delay effects on stability: a robust control approach, (2001), Springer Germany, Heidelberg |

[27] | Richard, J.P., Time-delay systems: an overview of some recent advances and open problems, Automatica, 39, 10, 1667-1694, (2003) · Zbl 1145.93302 |

[28] | Seiler, P.; Sengupta, R., An \(H_\infty\) approach to networked control, IEEE transactions on automatic control, 50, 3, 356-364, (2005) · Zbl 1365.93147 |

[29] | Walsh, G.C.; Ye, H.; Bushnell, L., Stability analysis of networked control systems, IEEE transactions on control systems technology, 10, 3, 438-446, (2002) |

[30] | Wang, Z.; Burnham, K.J., Robust filtering for a class of stochastic uncertain nonlinear time-delay systems via exponential state estimation, IEEE transactions on signal processing, 49, 4, 794-804, (2001) |

[31] | Wang, Z.; Huang, B.; Unbehauen, H., Robust \(H_\infty\) observer design of linear state delayed systems with parametric uncertainty: the discrete-time case, Automatica, 35, 1161-1167, (1999) · Zbl 1041.93514 |

[32] | Wu, M.; He, Y.; She, J.H.; Liu, G.P., Delay-dependent criteria for robust stability of time-varying delay systems, Automatica, 40, 1435-1439, (2004) · Zbl 1059.93108 |

[33] | Xia, Y.; Jia, Y., Robust stability functionals of state delayed systems with polytopic type uncertainties via parameter-dependent Lyapunov functions, International journal of control, 75, 1427-1434, (2002) · Zbl 1078.93054 |

[34] | Xu, S.; Lam, J.; Huang, S.; Yang, C., \(H_\infty\) model reduction for linear time-delay systems: continuous-time case, International journal of control, 74, 11, 1062-1074, (2001) · Zbl 1022.93008 |

[35] | Yang, F.W.; Wang, Z.D.; Hung, Y.S.; Gani, M., \(H_\infty\) control for networked systems with random communication delays, IEEE transactions on automatic control, 51, 3, 511-518, (2006) · Zbl 1366.93167 |

[36] | Yu, M.; Wang, L.; Chu, T., Sampled-data stabilization of networked control systems with nonlinearity, IEE Proceedings part D: control theory and applications, 152, 6, 609-614, (2005) |

[37] | Yu, M.; Wang, L.; Chu, T.; Hao, F., Stabilization of networked control systems with data packet dropout and transmission delays: continuous-time case, European journal of control, 11, 1, 40-55, (2005) · Zbl 1293.93622 |

[38] | Yue, D.; Han, Q.-L.; Lam, J., Network-based robust \(H_\infty\) control of systems with uncertainty, Automatica, 41, 6, 999-1007, (2005) · Zbl 1091.93007 |

[39] | Yue, D.; Han, Q.-L.; Peng, C., State feedback controller design of networked control systems, IEEE transactions on circuits and systems (II), 51, 11, 640-644, (2004) |

[40] | Zhang, L.; Shi, Y.; Chen, T.; Huang, B., A new method for stabilization of networked control systems with random delays, IEEE transactions on automatic control, 50, 8, 1177-1181, (2005) · Zbl 1365.93421 |

[41] | Zhang, W.; Branicky, M.; Phillips, S., Stability of networked control systems, IEEE control systems magazine, 21, 84-99, (2001) |

[42] | Zhang, X.-M.; Wu, M.; She, J.-H.; He, Y., Delay-dependent stabilization of linear systems with time-varying state and input delays, Automatica, 41, 8, 1405-1412, (2005) · Zbl 1093.93024 |

[43] | Zhivoglyadov, P.V.; Middleton, R.H., Networked control design for linear systems, Automatica, 39, 4, 743-750, (2003) · Zbl 1022.93018 |

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