An LMI approach to networked control systems with data packet dropout and transmission delays

The problem of data packet dropout and transmission delays induced by communication channel in networked control systems (NCSs) in both continuous-time case and discrete-time case is studied in this paper. We model the NCSs with data packet dropout and delays as ordinary linear systems with input delays and this enables us to apply the rich theory of delay systems to analysis and design of such NCSs. For the continuous-time case, our technique is based on Lyapunov-Razumikhin function method. For the discrete-time case, we use the Lyapunov-Krasovskii based method. Attention is focused on the design of memoryless state feedback controllers that guarantee stability of the closed-loop systems. We present the admissible bounds of data packet loss and of delays in terms of linear matrix inequalities. Numerical examples illustrate the effectiveness of the proposed approach.

[1]  Austin Blaquière,et al.  Nonlinear System Analysis , 1966 .

[2]  I. Petersen.  A stabilization algorithm for a class of uncertain linear systems , 1987 .

[3]  Asok Ray,et al.  Integrated Communication and Control Systems: Part II—Design Considerations , 1988 .

[4]  Asok Ray,et al.  An observer-based compensator for distributed delays , 1990, Autom..

[5]  Jack K. Hale,et al.  Introduction to Functional Differential Equations , 1993, Applied Mathematical Sciences.

[6]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[7]  Roger W. Brockett,et al.  Stabilization of motor networks , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[8]  Umit Ozguner,et al.  Closed-loop control of systems over a communications network with queues , 1995 .

[9]  Minyue Fu,et al.  Delay-dependent closed-loop stability of linear systems with input delay: an LMI approach , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[10]  R. Brockett,et al.  Systems with finite communication bandwidth constraints. I. State estimation problems , 1997, IEEE Trans. Autom. Control..

[11]  Johan Nilsson,et al.  Real-Time Control Systems with Delays , 1998 .

[12]  M. Branicky.  Multiple Lyapunov functions and other analysis tools for switched and hybrid systems , 1998, IEEE Trans. Autom. Control..

[13]  Kristi A. Morgansen,et al.  Limited communication control , 1999 .

[14]  Ho-Chan Kim,et al.  Hinfinity control of discrete-time linear systems with time-varying delays in state , 1999, Autom..

[15]  Wing Shing Wong,et al.  Systems with finite communication bandwidth constraints. II. Stabilization with limited information feedback , 1999, IEEE Trans. Autom. Control..

[16]  Linda Bushnell,et al.  Stability analysis of networked control systems , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[17]  Wei Zhang,et al.  Stability of networked control systems: explicit analysis of delay , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[18]  D. Hristu.  Stabilization of LTI systems with communication constraints , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[19]  Emilia Fridman,et al.  New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems , 2001, Syst. Control. Lett..

[20]  Li Yu,et al.  Optimal guaranteed cost control of discrete-time uncertain systems with both state and input delays , 2001, J. Frankl. Inst..

[21]  James Moyne,et al.  Analysis and modeling of networked control systems: MIMO case with multiple time delays , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

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

[23]  Michael D. Lemmon,et al.  Robust performance of soft real-time networked control systems with data dropouts , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[24]  Bruce A. Francis,et al.  Stabilizing a linear system by switching control with dwell time , 2002, IEEE Trans. Autom. Control..

[25]  Jamal Daafouz,et al.  Stability analysis and control synthesis for switched systems: a switched Lyapunov function approach , 2002, IEEE Trans. Autom. Control..

[26]  Christoforos N. Hadjicostis,et al.  Feedback control utilizing packet dropping network links , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[27]  Nandit Soparkar,et al.  Trading computation for bandwidth: reducing communication in distributed control systems using state estimators , 2002, IEEE Trans. Control. Syst. Technol..

[28]  Bruce A. Francis,et al.  Limited Data Rate in Control Systems with Networks , 2002 .

[29]  B. Azimi-Sadjadi,et al.  Stability of networked control systems in the presence of packet losses , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[30]  Panos J. Antsaklis,et al.  On the model-based control of networked systems , 2003, Autom..

[31]  Long Wang,et al.  Output feedback control of networked control systems , 2003, SMC'03 Conference Proceedings. 2003 IEEE International Conference on Systems, Man and Cybernetics. Conference Theme - System Security and Assurance (Cat. No.03CH37483).

[32]  Bruce A. Francis,et al.  Quadratic stabilization of sampled-data systems with quantization , 2003, Autom..

[33]  Anthony Tzes,et al.  Development and experimental verification of a mobile client-centric networked controlled system , 2003, 2003 European Control Conference (ECC).

[34]  Shengyuan Xu,et al.  Robust H∞ control for uncertain discrete-time systems with time-varying delays via exponential output feedback controllers , 2004, Syst. Control. Lett..