Stability Of Nonlinear Uncertain Lipschitz Systems Over The Digital Noiseless Channel

Document Type : Article

Author

Department of Electrical Engineering, Sharif University of Technology, Tehran, Iran

Abstract

This paper is concerned with the stability of nonlinear Lipschitz systems subject to bounded process
and measurement noises when transmission from sensor to controller is subject to distortion due to
quantization. A stabilizing technique and a sufficient condition relating transmission rate to Lipschitz
coefficients are presented for almost sure asymptotic bounded stability of nonlinear uncertain Lipschitz
systems. In the absence of process and measurement noises, it is shown that the proposed stabilizing
technique results in almost sure asymptotic stability. Computer simulations illustrate the satisfactory
performance of the proposed technique for almost sure asymptotic bounded stability and asymptotic
stability.

Keywords

Main Subjects


References
1. Canudas-de-Wit, C., Rubio, F.R., and Corchero, A. \A
new mechanism for controlling stick-slip oscillations in
oil well drill strings", IEEE Transactions on Control
Systems Technology, 16(6), pp. 1177-1191 (2008).
2. Memarzadeh, A. \Optimal borehole communication
using multicarrier modulation", Ph.D. Thesis, Rice
University (2008).
3. Elia, N. \When Bode meets Shannon: control-oriented
feedback communication schemes", IEEE Trans. Automat.
Contr., 49(9), pp. 1477-1488 (2004).
4. Elia, N. and Eisenbeis, J.N. \Limitations of linear
control over packet drop networks", IEEE Trans.
Automat. Contr., 56(4), pp. 826-841 (2011).
5. Martins, N.C., Dahleh, A., and Elia, N. \Feedback
stabilization of uncertain systems in the presence of
a direct link", IEEE Trans. Automat. Contr., 51(3),
pp. 438-447 (2006).
6. Minero, P., Franceschetti, M., Dey, S. and Nair, N.
\Data rate theorem for stabilization over time-varying
feedback channels", IEEE Trans. Automat. Contr.,
54(2), pp. 243-255 (2009).
7. Minero, P., Coviello, L., and Franceschetti, M. \Stabilization
over Markov feedback channels: the general
case", IEEE Trans. Automat. Contr., 58(2), pp. 349-
362 (2013).
8. Farhadi, A. \Stability of linear dynamic systems controlled
over the packet erasure channel: a co-design
approach", International Journal of Control, 88(12),
pp. 2488-2498 (2015).
9. Farhadi, A. \Feedback channel in linear noiseless
dynamic systems controlled over the packet erasure
network", International Journal of Control, 88(8), pp.
1490-1503 (2015).
10. Farhadi, A., Domun, J. and Canudas de Wit, C. \A
supervisory control policy over an acoustic communication
network", International Journal of Control, 88(5),
pp. 946-958 (2015).
11. Niu, Y. and Ho, D.W.C. \Control strategy with
adaptive quantizer's parameters under digital communication
channels", Automatica, 50(10), pp. 2665-2671
(2014).
12. Nair, G.N., Evans, R.J., Mareels, I.M.Y., and Moran,
W. \Topological feedback entropy and nonlinear stabilization",
IEEE Trans. Automat. Contr., 49(9), pp.
1585-1597 (2004).
13. Nair, G.N. and Evans, R.J. \Stabilizability of stochastic
linear systems with nite feedback data rates",
SIAM J. Control Optimization, 43(3), pp. 413-436
(2004).
14. Canudas de Wit, C., Gomez-Estern, F. and Rodrigues
Rubio, F. \Delta-modulation coding redesign
for feedback-controlled systems", IEEE Transactions
on Industrial Electronics, 56(7), pp. 2684-2696 (2009).
15. Nair, G.N. and Evans, R.J. \State estimation via a
capacity limited communication channel", IEEE Conf.
Decision Contr., pp. 866-871 (1997).
16. Farhadi, A. and Ahmed, N.U. \Tracking nonlinear
noisy dynamic systems over noisy communication
channels", IEEE Transactions on Communications,
59(4), pp. 955-961 (2011).
17. Tatikonda, S. and Mitter, S. \Control over noisy
channels", IEEE Transactions on Automatic Control,
49(7), pp. 1196-1201 (2004).
Volume 25, Issue 3
Transactions on Computer Science & Engineering and Electrical Engineering (D)
May and June 2018
Pages 1523-1532
  • Receive Date: 31 October 2015
  • Revise Date: 25 September 2016
  • Accept Date: 16 January 2017