Output feedback stabilization for Markov-based nonuniformly sampled-data networked control systems

Abstract This paper investigates the issue of output feedback stabilization for networked control systems. The randomly sampled measurement process caused by the time-varying channel load is modeled as a Markov chain. An event-driven transmitter, which depends on the measurement sampling period, is introduced to transmit the control signal. In order to achieve a less conservative result, a novel output feedback controller, including both sampling and event-driven transmitter-induced delay indexes, is proposed. The sufficient and necessary condition for the mean-square stability, the stochastic stability, and the exponential mean-square stability for the closed-loop system is established, and the controller is designed by using the cone complementarity linearization approach. Finally, based on the ZigBee real communication channel, a cart and inverted pendulum system is shown to demonstrate the effectiveness of the proposed method.

[1]  K. Loparo,et al.  Stability and control of discrete-time jump linear systems , 1991 .

[2]  A. Hassibi,et al.  Control with random communication delays via a discrete-time jump system approach , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[3]  Yang Shi,et al.  Output Feedback Stabilization of Networked Control Systems With Random Delays Modeled by Markov Chains , 2009, IEEE Transactions on Automatic Control.

[4]  Jing Wu,et al.  Design of Networked Control Systems With Packet Dropouts , 2007, IEEE Transactions on Automatic Control.

[5]  Huijun Gao,et al.  I filtering for 2D Markovian jump systems , 2008, Autom..

[6]  Bor-Sen Chen,et al.  Robust H∞ filtering for nonlinear stochastic systems , 2005 .

[7]  Hisaya Fujioka.  Stability analysis of systems with aperiodic sample-and-hold devices , 2009, Autom..

[8]  Robin J. Evans,et al.  Feedback Control Under Data Rate Constraints: An Overview , 2007, Proceedings of the IEEE.

[9]  L. Ghaoui,et al.  A cone complementarity linearization algorithm for static output-feedback and related problems , 1996, Proceedings of Joint Conference on Control Applications Intelligent Control and Computer Aided Control System Design.

[10]  Tongwen Chen,et al.  H∞ filtering for nonuniformly sampled systems , 2010, CCECE 2010.

[11]  Dawn M. Tilbury,et al.  The Emergence of Industrial Control Networks for Manufacturing Control, Diagnostics, and Safety Data , 2007, Proceedings of the IEEE.

[12]  Wei Zhang,et al.  Stability of networked control systems , 2001 .

[13]  Ya-Jun Pan,et al.  A New Predictive Approach for Bilateral Teleoperation With Applications to Drive-by-Wire Systems , 2006, IEEE Transactions on Robotics.

[14]  Bo Yu,et al.  Modified Generalized Predictive Control of Networked Systems With Application to a Hydraulic Position Control System , 2011 .

[15]  W. L. Koning,et al.  Discrete-time Markovian jump linear systems , 1993 .

[16]  Bo Yu,et al.  Robust mixed H2/H∞ control of networked control systems with random time delays in both forward and backward communication links , 2011, Autom..

[17]  W. P. M. H. Heemels,et al.  Controller synthesis for networked control systems , 2010, Autom..

[18]  Li Qiu,et al.  Linear periodically time-varying discrete-time systems: aliasing and LTI approximations , 1997 .

[19]  Masayoshi Tomizuka,et al.  Variable sampling rate controller design for brushless DC motor , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[20]  Emilia Fridman,et al.  A refined input delay approach to sampled-data control , 2010, Autom..

[21]  Masayoshi Tomizuka,et al.  Multirate estimation and control under time-varying data sampling with applications to information storage devices , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[22]  Tariq Samad,et al.  Network-Centric Systems for Military Operations in Urban Terrain: The Role of UAVs , 2007, Proceedings of the IEEE.

[23]  J.P. Hespanha,et al.  On the robust stability and stabilization of sampled-data systems: A hybrid system approach , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[24]  Huiping Li,et al.  Robust H∞ filtering for nonlinear stochastic systems with uncertainties and Markov delays , 2012, Autom..

[25]  Tongwen Chen,et al.  A new method for stabilization of networked control systems with random delays , 2005 .

[26]  T. Burchfield,et al.  Maximizing Throughput in ZigBee Wireless Networks through Analysis , Simulations and Implementations * , 2007 .

[27]  Bruce A. Francis,et al.  Optimal Sampled-Data Control Systems , 1996, Communications and Control Engineering Series.

[28]  Raja Sengupta,et al.  An H/sub /spl infin// approach to networked control , 2005, IEEE Transactions on Automatic Control.

[29]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[30]  João Pedro Hespanha,et al.  A Survey of Recent Results in Networked Control Systems , 2007, Proceedings of the IEEE.

[31]  Yugang Niu,et al.  Stabilization of Markovian jump linear system over networks with random communication delay , 2009, Autom..