# zbMATH — the first resource for mathematics

Robust dissipative control for internet-based switching systems. (English) Zbl 1298.93138
Summary: A class of hybrid multi-rate control models with time-delay and switching controllers are formulated based on combined remote control and local control strategies. The problem of robust dissipative control for this discrete system is investigated. An improved Lyapunov-Krasovskii functional is constructed and the subsequent analysis provides some new sufficient conditions in the form of LMIs for both nominal and uncertain representations. Several special cases of practical interests are derived. A numerical simulation example is given to illustrate the effectiveness of the theoretical result.

##### MSC:
 93B35 Sensitivity (robustness) 93C55 Discrete-time control/observation systems 93C05 Linear systems in control theory 68M11 Internet topics
Full Text:
##### References:
 [1] Montestruque, L.A.; Antsaklis, P.J., On the model-based control of networked systems, Automatica, 39, 1837-1843, (2003) · Zbl 1027.93023 [2] Montestruque, L.A.; Antsaklis, P.J., Stability of model-based networked control systems with time-varying transmission times, IEEE transactions on automatic control, 49, 9, 1562-1573, (2004) · Zbl 1365.90039 [3] Nesic, D.; Teel, A.R., Input-to-state stability of networked control systems, Automatica, 40, 2121-2128, (2004) · Zbl 1077.93049 [4] Overstreet, J.W.; Tzes, A., An Internet-based real-time control engineering laboratory, IEEE control systems magazine, 19, 320-326, (1999) [5] Srinivasagupta, D.; Joseph, B., Internet-mediated process control laboratory, IEEE control systems magazine, 23, 110-118, (2003) [6] Guo, S.; Feng, G.; Liao, X.; Liu, Q., Novel delay-range-dependent stability analysis of the second-order congestion control algorithm with heterogonous communication delays, Journal of network and computer applications, 32, 568-577, (2009) [7] Wang, F.Y.; Liu, D., Networked control systems: theory and applications, (2008), Springer London [8] Yang, S.H.; Chen, X.; Alty, J.L., Design issues and implementation of Internet-based process control systems, Control engineering practice, 11, 709-720, (2003) [9] Yang, S.H.; Chen, X.; Tan, L.; Yang, L., Time-delay and data loss compensation for Internet-based process control systems, Transactions of the institute of measurement and control, 27, 103-108, (2005) [10] S.H. Yang, C. Dai, Multi-rate control in Internet-based control systems, in: M.N. Sahinkaya, K.A. Edge (Eds.), Proceedings of the UK Control, Bath, UK, 2004, ID-053. [11] M.S. Mahmoud, A. Ismail, Role of delay in networked control systems, in: Proceedings of the 10th IEEE International Conference on Electronics, Circuits and Systems, UoS, UAE, December 15-17, 2003, pp. 40-43. [12] Gao, H.; Chen, T.; Lam, J., A new delay system approach to network-based control, Automatica, 44, 39-52, (2008) · Zbl 1138.93375 [13] Seiler, P.; Sengupta, R., An $$\mathcal{H}_\infty$$ approach to networked control, IEEE transactions on automatic control, 50, 356-364, (2005) · Zbl 1365.93147 [14] Han, K.H.; Kim, S.; Kim, Y.J.; Kim, J.H., Internet control architecture for Internet-based personal robot, Autonomous robots, 10, 135-147, (2001) · Zbl 1030.68685 [15] Zhang, W.; Branicky, M.S.; Phillips, S.M., Stability of networked control systems, IEEE control systems magazine, 21, 84-99, (2001) [16] 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, 1177-1181, (2005) · Zbl 1365.93421 [17] Hill, D.J.; Moylan, P.J., Dissipative dynamical systems: basic input – output and state properties, Journal of the franklin institute, 309, 327-357, (1980) · Zbl 0451.93007 [18] Lozano, R.; Brogliato, B.; Egeland, O.; Maschke, B., Dissipative systems analysis and control: theory and applications, (2000), Springer London · Zbl 0958.93002 [19] Mahmoud, M.S.; Abdulla, I., Passivity analysis and synthesis of discrete-time delay systems, Journal of dynamics of continuous, discrete and impulsive systems, series A, 11, 4, 502-525, (2004) · Zbl 1175.93141 [20] Mahmoud, M.S.; Abdulla, I., New results on delay-dependent control of time-delay systems, IEEE transactions on automatic control, 50, 95-100, (2005) · Zbl 1365.93143 [21] Park, J.H., Robust stabilization for dynamic systems with multiple time-varying delays and nonlinear uncertainties, Journal of optimization theory and applications, 108, 1, 155-174, (2001) · Zbl 0981.93069 [22] Park, J.H.; Won, S., Asymptotic stability of neutral systems with multiple delays, Journal of optimization theory and applications, 103, 1, 183-200, (1999) · Zbl 0947.65088 [23] Park, J.H.; Won, S., A note on stability of neutral delay-differential systems, Journal of the franklin institute, 336, 3, 543-548, (1999) · Zbl 0969.34066 [24] Yue, D.Q.; Han, L.; Lam, J., Network-based robust $$\mathcal{H}_\infty$$ control of systems with uncertainty, Automatica, 41, 999-1007, (2005) · Zbl 1091.93007 [25] S. Boyd, L. El Ghaoui, E. Feron, V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, in: SIAM Studies in Applied Mathematics, Philadelphia, 1994. · Zbl 0816.93004
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.