On Polytopic Approximations of Systems with Time-Varying Input Delays

Networked control systems (NCS) have recently received an increasing attention from the control systems community. One of the major problems in NCS is how to model the highly nonlinear terms caused by uncertain delays such as time-varying input delays. A straightforward solution is to employ polytopic approximations. In this paper we develop a novel method for creating discrete-time models for systems with time-varying input delays based on polytopic approximations. The proposed method is compared to several other existing approaches in terms of quality, complexity and scalability. Furthermore, its suitability for model predictive control is demonstrated.

[1]  Stephen P. Boyd,et al.  Future directions in control in an information-rich world , 2003 .

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

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

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

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

[6]  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).

[7]  Peter Lancaster,et al.  The theory of matrices , 1969 .

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

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

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