We address stabilization problems of networked control systems in the presence of bounded packet losses and time-varying network-induced delays. When the delay is less than the transmission interval, we prove that the stability of the closed-loop system is implied by that of a switched system. Based on theories on switched systems, we present stabilizing conditions by using packet-loss-dependent Lyapunov functions, and design multiple controllers depending on the packet loss and the network-induced delay. Furthermore, based on the stabilizing conditions, we discuss the robustness of the stabilization against the packet loss and the network-induced delay. Several numerical examples and simulations are worked out to demonstrate the effectiveness of the proposed design approach.
BranickyMSPhillipsSRZhangW (2000) Stability of networked control systems: Explicit analysis of delay. In: Proceedings of the American Control Conference, Chicago, IL, pp. 2352–2357.
2.
DaafouzJRiedingerPIungC (2002) Stability analysis and control synthesis for switched systems: A switched Lyapunov function approach. IEEE Transactions on Automatic Control47: 1883–1887.
3.
DaiL (1989) Singular Control Systems (Lecture Notes in Control and Information Sciences). Berlin: Springer-Verlag.
4.
FridmanE (2001) New Lyapunov–Krasovskii functionals for stability of linear retarded and neutral type systems. Systems Control Letters43: 309–319.
5.
GaoHChenTLamJ (2008) A new delay system approach to network-based control. Automatica44: 39–52.
6.
GhaouiLEOustryFRamiMA (1997) A cone complementarity linearization algorithm for static output-feedback and related problems. IEEE Transactions on Automatic Control42: 1171–1176.
7.
GuanZZhanXFengG (2012) Optimal tracking performance of MIMO discrete-time systems with communication constraints, International Journal of Robust and Nonlinear Control22: 1429–1439.
8.
HouLZongGWuY (2012) Exponential I2 − I∞ output tracking control for discrete-time switched system with time-varying delay. International Journal of Robust and Nonlinear Control22: 1175–1194.
9.
HuSYanW (2007) Stability robustness of networked control systems with respect to packet loss. Automatica43: 1243–1248.
10.
LiberzonD (2003) Switching in Systems and Control. Boston, MA: Birkhäuser.
11.
LinHZhaiGAntsaklisPJ (2006) Asymptotic stability and disturbance attenuation properties for a class of networked control systems. Journal of Control Theory and Applications1: 76–85.
12.
MatveevASSavkinAV (2006) Multirate stabilisation of linear multiple sensor systems via limited capacity communication channels, SIAM Journal on Control and Optimization, 44(2): 584–617.
13.
MontestruqueLAAntsaklisPJ (2003) On the model-based control of networked systems. Automatica39: 1837–1843.
14.
PhatVNRatchagitK (2011) Stability and stabilization of switched linear discrete-time systems with interval time-varying delay. Nonlinear Analysis: Hybrid Systems5: 605–612.
15.
SunJLiuG (2006) State feedback control of networked systems-an LMI approach. In: Proceedings IEEE International Conference on Networking, Sensing and Control, Ft Lauderdale, FL, pp. 637–642.
16.
WalshGCHongYBushnellLG (2002) Stability analysis of networked control systems. IEEE Transactions on Control Systems Technology10: 438–446.
17.
WangYYangG (2007) H∞ control of networked control systems with time delay and packet disordering. IET Control Theory and Applications1: 1344–1354.
18.
WongWSBrockettRW (1999) Systems with finite communication bandwidth constraints–-II. Stabilization with limited information feedback. IEEE Transactions on Automatic Control44: 1049–1053.
19.
WuJChenT (2007) Design of networked control systems with packet dropouts. IEEE Transactions on Automatic Control52: 1314–1319.
20.
XiaoNXieLQiuL (2012) Feedback stabilization of discrete-time networked systems over fading channels. IEEE Transactions on Automatic Control57: 2176–2189.
21.
XiongJLamJ (2007) Stabilisation of linear systems over networks with bounded packet loss. Automatica43: 80–87.
22.
XueBLiSZhuQ (2012) Moving horizon state estimation for networked control systems with multiple packet dropouts. IEEE Transactions on Automatic Control57: 2360–2366.
23.
YuMWangLChuTXieG (2004) Stabilisation of networked control systems with data packet dropout and network delays via switching system approach. In: Proceedings 43rd IEEE Conference on Decision and Control, Nassau, Bahamas, pp. 3539–3544.
24.
ZhangWBranickyMSPhillipsSM (2001) Stability of networked control systems. IEEE Control Systems Magazine21: 84–99.
25.
ZhangWYuL (2007) Output feedback stabilization of networked control systems with packet dropouts. IEEE Transactions on Automatic Control52: 1705–1710.
26.
ZongGHouLLiJ (2011) A descriptor system approach to filtering for uncertain discrete-time switched system with mode-dependent time-varying delays. International Journal of Innovative Computing, Information and Control 7(5A): 2213–2224.
27.
ZongGHouLWuY (2012) Exponential I2 − I∞ filtering for discrete-time switched systems under a new framework. Journal of Adaptive Control and Signal Processing26: 124–137.
