Abstract
The problem of guaranteed cost control for the networked control systems (NCSs) with time-varying delays, time-varying sampling intervals and signals quantization was investigated, wherein the physical plant was continuous-time one, and the control input was discrete-time one. By using an input delay approach and a sector bound method, the network induced delays, quantization parameter and sampling intervals were presented in one framework in the case of the state and the control input by quantized in a logarithmic form. A novel Lyapunov function with discontinuity, which took full advantages of the NCS characteristic information, was exploited. In addition, it was shown that Lyapunov function decreased at the jump instants. Furthermore, the Leibniz-Newton formula and free-weighting matrix methods were used to obtain the guaranteed cost controller design conditions which were dependent on the NCS characteristic information. A numerical example was used to illustrate the effectiveness of the proposed methods.
Similar content being viewed by others
References
CLOOSTERMAN M, HETEL L, de WOUWA N, HEEMELSAW, DAAFOUZ J, NIJMEIJER H. Controller synthesis for networked control systems [J]. Automatica, 2010, 46: 1584–1594.
WANG Rui, LIU Guo-ping, WANG Wei, REES D, ZHAO Yun-Bo. Guaranteed cost control for networked control systems based on improved predictive control method [J]. IEEE Transactions on Control Systems Technology, 2010, 18(5): 1226–1232.
HUA Chang-chun, YE Cai-hong, GUAN Xin-ping. Quantized guaranteed cost control for wireless networked control system [C]//. Proceedings of the 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference. Shanghai, 2009, 2028–2032.
HU Li-sheng, BAI Tao, SHI Peng, WU Zi-ming. Sampled-data control of networked linear control systems [J]. Automatica, 2007, 43: 903–911.
YANG Hong-jiu, XIA Yuan-qing, SHI Peng. Stabilization of networked control systems with nonuniform random sampling periods [J]. International Journal of Robust and Nonlinear Control, 2011, 21(5): 501–526.
NAGHSHTABRIZI P, HESPANHA J. Designing an observer-based controller for a network control system [C]//. Proceedings of The 44th IEEE Conference on Decision and Control, and the European Control Conference. Seville, Spain, 2005: 848–853.
YANG De-dong, CAI Kai-yuan. Reliable guaranteed cost sampling control for nonlinear time-delay systems [J]. Mathematics and Computers in Simulation, 2010, 80: 2005–2018.
YANG Rong-ni, SHI Peng, LIU Guo-ping, GAO Hui-jun. Network-based feedback control for systems with mixed delays based on quantization and dropout compensation [J]. Automatica, 2011, 47: 2805–2809.
ISHIDO Y, TAKABA K, QUEVEDO D. Stability analysis of networked control systems subject to packet-dropouts and finite-level quantization [J]. Systems & Control Letters, 2011, 60: 325–332.
LIU Ming, WANG Qing-ling, LI Hong-yi. State estimation and stabilization for nonlinear networked control systems with limited capacity channel [J]. Journal of the Franklin Institute, 2011, 348: 1869–1885.
SUN Jian, LIU Guo-ping, CHEN Jie, REES D. Improved delay-range-dependent stability criteria for linear systems with time-varying delays [J]. Automatica, 2010, 46: 466–470.
GAO Hui-Jun, CHEN Tong-Wen, LAM J. A new delay system approach to network-based control [J]. Automatica, 2008, 44: 39–52.
DAI Jian-guo. A delay system approach to networked control systems with limited communication capacity [J]. Journal of the Franklin Institute, 2010, 34(7): 1334–1352.
FRIDMAN E. A refined input delay approach to sampled-data control [J]. Automatica, 2010, 46: 421–427.
ELIA N, MITTER S. Stabilization of linear systems with limited information [J]. IEEE Transactions on Automatic Control, 2001, 46(9): 1384–1400.
FU Min-rui, XIE Li-hua. The sector bound approach to quantized feedback control [J]. IEEE Transactions on Automatic Control, 2005, 50(11): 1698–1711.
GHAOUI L, OUSTRY F, AITRAMI M. A cone complementarity linearization algorithm for static output-feedback and related problems [J]. IEEE Transactions on Automatic Control, 1997, 46: 1171–1176
Author information
Authors and Affiliations
Corresponding author
Additional information
Foundation item: Project(61104106) supported by the National Natural Science Foundation of China; Project(201202156) supported by the Natural Science Foundation of Liaoning Province, China; Project(LJQ2012100) supported by Program for Liaoning Excellent Talents in University (LNET)
Rights and permissions
About this article
Cite this article
Liu, Yy., Chu, Yk. & Che, Ww. Guaranteed cost control of networked control systems under limited communication capacity and variable sampling. J. Cent. South Univ. 21, 978–986 (2014). https://doi.org/10.1007/s11771-014-2027-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11771-014-2027-z