# zbMATH — the first resource for mathematics

Modelling and control of networked control systems with both network-induced delay and packet-dropout. (English) Zbl 1153.93321
Summary: A new switched linear system model is proposed to describe the Networked Control System (NCS) with both network-induced delay and packet-dropout. A sufficient condition is derived for the exponential stability of the closed-loop NCS, and the obtained condition establishes the quantitative relation between the packet-dropout rate and the stability of the NCS. Design procedures for the state feedback stabilising controllers are also presented by using the augmenting technique. An illustrative example is provided to demonstrate the effectiveness of the proposed method.

##### MSC:
 93A30 Mathematical modelling of systems (MSC2010) 90B10 Deterministic network models in operations research 93C55 Discrete-time control/observation systems 93B51 Design techniques (robust design, computer-aided design, etc.) 90B18 Communication networks in operations research
Full Text:
##### References:
 [1] Gao, H.J.; Chen, T.; Lam, J., A new delay system approach to network-based control, Automatica, 44, 1, 39-52, (2008) · Zbl 1138.93375 [2] Garcia-Rivera, M.; Barreiro, A., Analysis of networked control systems with drops and variable delays, Automatica, 43, 12, 2054-2059, (2007) · Zbl 1138.93349 [3] Hu, L.S.; Bai, T.; Shi, P.; Wu, Z.M., Sampled-data control of networked linear control systems, Automatica, 43, 5, 903-911, (2007) · Zbl 1117.93044 [4] Hu, S.S.; Zhu, Q.X., Stochastic optimal control and analysis of stability of networked control systems with long delays, Automatica, 39, 11, 1877-1884, (2003) · Zbl 1175.93240 [5] Kim, D.S.; Lee, Y.S.; Kwon, W.H.; Park, H.S., Maximum allowable delay bounds of networked control systems, Control engineering practice, 11, 11, 1301-1313, (2003) [6] Lin, H.; Antsaklis, P.J., Stability and persistent disturbance attenuation properties for a class of networked control systems: switched system approach, International journal of control, 78, 18, 1447-1458, (2005) · Zbl 1122.93357 [7] Liu, G.P.; Mu, J.X.; Rees, D.; Chai, S.C., Design and stability of networked control systems with random communication time delay using the modified MPC, International journal of control, 79, 4, 288-297, (2006) · Zbl 1140.93394 [8] Lian, F.L. (2001). Analysis, design, modeling and control of networked control systems. Ph.D. thesis. Department of Mechanical Engineering, University of Michigan [9] Martins, N.C.; Dahleh, M.A.; Elia, N., Feedback stabilization of uncertain systems in the presence of a direct link, IEEE transactions on automatic control, 51, 3, 438-447, (2006) · Zbl 1366.93516 [10] Matveev, A.S.; Savkin, A.V., Multi-rate stabilization of linear multiple sensor systems via limited capacity communication channels, SIAM journal on control and optimization, 44, 2, 584-618, (2005) · Zbl 1130.93405 [11] Matveev, A.S.; Savkin, A.V., An analogue of Shannon information theory for detection and stabilization via noisy discrete communication channels, SIAM journal on control and optimization, 46, 4, 1323-1361, (2007) · Zbl 1140.93016 [12] Nilsson, J. (1998). Real-time control systems with delays. Ph.D. thesis. Lund, Sweden: Lund Institute of Technology · Zbl 0908.93073 [13] Seiler, P.; Sengupta, R., An $$H_\infty$$ approach to networked control, IEEE transactions on automatic control, 50, 3, 356-364, (2005) · Zbl 1365.93147 [14] Tatikonda, S.; Mitter, S., Control over noisy channels, IEEE transactions on automatic control, 49, 7, 1196-1201, (2004) · Zbl 1365.94341 [15] Xiong, J.L.; Lam, J., Stabilization of linear systems over networks with bounded packet loss, Automatica, 43, 1, 80-87, (2007) · Zbl 1140.93383 [16] Yue, D.; Han, Q.L.; Chen, P., State feedback controller design of networked control systems, IEEE transactions on circuits and systems II: express briefs, 51, 11, 640-644, (2004) [17] Zhai, G.S., Hu, B., Yasuda, K., & Michel, A. (2002). Qualitative analysis of discrete-time switched systems. In Proceedings of the American control conference (pp. 1880-1885) [18] Zhang, W.A.; Yu, L., Output feedback stabilization of networked control systems with packet dropouts, IEEE transactions on automatic control, 52, 9, 1705-1710, (2007) · Zbl 1366.93543
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.