# zbMATH — the first resource for mathematics

Sampled-data control of networked linear control systems. (English) Zbl 1117.93044
Summary: The problem of synthesis and analysis for the networked control systems (NCSs) with time-driven digital controllers and event-driven holders is considered. The NCS is modelled as a sampled-data system with time-delay in its discrete-time subsystem. This model is able to capture many network-induced features, for example, time-delay and packet dropout. Moreover, the model allows different combinations of the time-driven or event-driven mode of the devices, including the samplers, the controllers and the holders. By transforming time-delay in the discrete-time subsystem into its continuous-time subsystem of the sampled-data system, we have also obtained a less conservative time-delay dependent stability result for the NCSs, using a new Lyapunov function and a relaxed condition. Some limitations of the existing literatures on network-induced time-delay and sampling period are removed in the proposed framework. Furthermore, a sampled-data control design procedure is developed for the NCSs. Linear matrix inequality approach has been employed to solve the stability and control design problems. Finally, numerical examples are included to demonstrate the effectiveness of the proposed stability result and the potential of the proposed techniques.

##### MSC:
 93C55 Discrete-time control/observation systems 93B52 Feedback control 93D30 Lyapunov and storage functions
Full Text:
##### References:
 [1] Boukas, E.K., Stabilization of stochastic nonlinear hybrid systems, International journal of innovative computing, information and control, 1, 1, 131-141, (2005) · Zbl 1085.93026 [2] Boukas, E.K.; Al-Muthairi, N.F., Delay-dependent stabilization of singular linear systems with delays, International journal of innovative computing, information and control, 2, 2, 283-291, (2006) [3] Boyd, S.; El Ghaoui, L.; Feron, E.; Balakrishnan, V., Linear matrix inequalities in system and control theory, (1994), SIAM Philadelphia · Zbl 0816.93004 [4] Branicky, M.S.; Phillips, S.M.; Zhang, W., Scheduling and feedback co-design for networked control systems, Proceedings of American control conference, 2, 1211-1217, (2002) [5] Chen, B.; Lam, J.; Xu, S., Memory state feedback guaranteed cost control for neutral delay systems, International journal of innovative computing, information and control, 2, 2, 293-303, (2006) [6] Chen, T.; Francis, B., Optimal sampled-data control systems, (1995), Springer Berlin · Zbl 0847.93040 [7] Cao, Y.-Y., Hu, L.-S. & Xu, A. (2004). A new delay-dependent stability condition and $$H_\infty$$ control for jump time-delay systems. Proceedings of American Control Conference, 4183-4188. [8] Fridman, E.; Seuret, A.; Richard, J.P., Robust sampled-data stabilization of linear systems: an input delay approach, Automatica, 40, 1441-1446, (2004) · Zbl 1072.93018 [9] Gu, K.; Niculescu, S.I., Additional dynamics in transformed time-delay systems, IEEE transactions on automatic control, 45, 3, 572-575, (2000) · Zbl 0986.34066 [10] Hu, L.-S.; Cao, Y.-Y.; Shao, H.-H., Constrained robust sampled-data control for nonlinear uncertain systems, International journal of robust and nonlinear control, 12, 5, 447-464, (2002) · Zbl 1026.93035 [11] Hu, L.-S.; Huang, B., Multirate robust control for fuzzy systems with periodic Lyapunov function, IEEE transactions on fuzzy systems, 13, 4, 436-443, (2005) [12] Hu, L.-S.; Huang, B.; Cao, Y.-Y., Robust digital model predictive control for linear uncertain systems with saturations, IEEE transactions on automatic. control, 49, 5, 792-796, (2004) · Zbl 1365.93279 [13] Hu, L.-S.; Lam, J.; Cao, Y.-Y.; Shao, H.-H., LMI approach to robust $$H_2$$ sampled-data control for linear uncertain systems, IEEE transactions of system, man and cybernet, part B, 33, 1, 149-155, (2003) [14] Hu, L.-S.; Shi, P.; Frank, P.M., Robust sampled-data control for Markovian jump linear systems, Automatica, 42, 2025-2030, (2006) · Zbl 1112.93057 [15] Hristu-Varsakelis, D., Feedback control systems as users of a shared network: communication sequences that guarantee stability, Proceedings of 40th conference on decision and control, 4, 3631-3636, (2001) [16] Hristu-Varsakelis, D.; Kumar, P.R., Interrupt-based feedback control over a shared communication medium, Proceedings of 41st conference on decision and control, 4, 3596-3601, (2002) [17] Halevi, Y.; Ray, A., Integrated communication and control systems: part I—analysis and part II—design consideration, ASME journal of dynamic system measurements and control, 110, 367-381, (1988) [18] Krtolica, R.; Oguner, U.; Chan, H., Stability of feedback systems with random communication delays, International journal of control, 59, 4, 925-953, (1994) · Zbl 0812.93073 [19] Ling, Q. & Lemmon, M.D. (2002). Robust performance of soft real-time networked control systems with data dropouts. Proceedings of 41st Conference on Decision and Control (pp. 1225-1230). Las Vegas. [20] 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 [21] Moon, Y.S.; Park, P.; Kwon, W.H.; Lee, Y.S., Delay-dependent robust stabilization of uncertain state-delayed systems, International journal of control, 74, 1447-1455, (2001) · Zbl 1023.93055 [22] Nilsson, J. (1998). Real-time control systems with delays. Ph.D. Thesis, Department of Automatic Control, Lund Institute of Technology. · Zbl 0908.93073 [23] Shi, P., Filtering on sampled-data systems with parametric uncertainty, IEEE transactions on automatic control, 43, 7, 1022-1027, (1998) · Zbl 0951.93050 [24] Shi, P.; Boukas, E.K.; Agarwal, R.; Shue, S., Robust control of linear continuous time-delay systems with finite discrete jumps and norm-bounded uncertainties, International journal of systems and sciences, 29, 12, 1381-1392, (1998) · Zbl 1065.93510 [25] Shi, P.; de Souza, C.E.; Xie, L., Bounded real lemma for linear systems with finite discrete jumps, International journal of control, 66, 1, 145-159, (1997) · Zbl 0871.93023 [26] Shi, P.; Fu, M.; de Souza, C.E., Loop transfer recovery for systems under sampled measurements, IEE-D, control theory and applications, 143, 4, 333-337, (1996) · Zbl 0863.93036 [27] Walsh, G.C.; Beldiman, O.; Bushnell, L.G., Stability analysis of networked control system, (), 2876-2880 [28] Walsh, G.C.; Ye, H.; Bushnell, L.G., Stability analysis of networked control systems, IEEE transactions on control systems technology, 10, 438-446, (2002) [29] Xie, L.; Shi, P.; de Souza, C.E., On designing controller for a class of uncertain sampled-data nonlinear systems, IEE-D, control theory and applications, 140, 2, 119-126, (1993) · Zbl 0773.93049 [30] Zhang, W. (2001). Stability analysis of networked control systems. Ph.D. Thesis, Department of Electrical Engineering and Computer Science, Case Western Reserve University, August 4, 2001. [31] Zhang, W.; Branicky, M.S.; Phillips, S.M., Stability of networked control systems, IEEE control and systems magazine, 21, 84-99, (2001)
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.