On polytopic inclusions as a modeling framework for systems with time-varying delays

One of the important issues in networked control systems is the appropriate handling of the nonlinearities arising from uncertain time-varying delays. In this paper, using the Cayley-Hamilton theorem, we develop a novel method for creating discrete-time models of linear systems with time-varying input delays based on polytopic inclusions. The proposed method is compared with existing approaches in terms of conservativeness, scalability and suitability for controller synthesis.

[1]  Cleve B. Moler,et al.  Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later , 1978, SIAM Rev..

[2]  Sorin Olaru,et al.  Predictive Control for Linear Systems with Delayed Input Subject to Constraints , 2008 .

[3]  Mircea Lazar,et al.  Stabilization of networked control systems via non-monotone control ^lyapunov functions , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[4]  Y. Tipsuwan,et al.  Control methodologies in networked control systems , 2003 .

[5]  Riaz A. Usmani.  Applied Linear Algebra , 1986 .

[6]  Arthur Cayley,et al.  II. A memoir on the theory of matrices , 1858, Philosophical Transactions of the Royal Society of London.

[7]  Nathan van de Wouw,et al.  Robust Stability of Networked Control Systems with Time-varying Network-induced Delays , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

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

[9]  Young Soo Suh.  Stability and stabilization of nonuniform sampling systems , 2008, Autom..

[10]  Jamal Daafouz,et al.  Stabilization of Arbitrary Switched Linear Systems With Unknown Time-Varying Delays , 2006, IEEE Transactions on Automatic Control.

[11]  M. Kothare,et al.  Robust constrained model predictive control using linear matrix inequalities , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[12]  Y. Shu.  Stability and stabilization of nonuniform sampling systems. , 2008 .

[13]  Jared R. Leadbetter,et al.  Control in an Information Rich World Report of the Panel on Future Directions in Control , Dynamics , and Systems , 2002 .

[14]  Nathan van de Wouw,et al.  Stability of Networked Control Systems With Uncertain Time-Varying Delays , 2009, IEEE Transactions on Automatic Control.

[15]  Nathan van de Wouw,et al.  Stability of networked control systems with large delays , 2007, 2007 46th IEEE Conference on Decision and Control.