218
Views
17
CrossRef citations to date
0
Altmetric
Original Articles

Stability of uncertain piecewise affine systems with time delay: delay-dependent Lyapunov approach

, &
Pages 1423-1434 | Received 28 Sep 2007, Accepted 01 Sep 2008, Published online: 18 Jun 2009

References

  • Aghdam , AG and Davison , EJ . 2003 . Pseudo-Decentralised Switching Control . Automatica , 39 : 317 – 324 .
  • Aghdam , AG and Davison , EJ . 2007 . Decentralised Switching Control for Hierarchical Systems . Automatica , 43 : 1092 – 1100 .
  • Azuma , S and Imura , J . 2003 . Optimal Control of Sampled-data Piecewise-affine Systems and its Application to CPU Processing Control . Proceedings of the 42th IEEE Conference on Decision Control . 2003 , Maui, Hawaii. pp. 161 – 166 .
  • Beccuti , AG , Papafotiou , G and Morari , M . 2005 . Optimal Control of the Boost dc–dc Converter . Proceedings of the 44th IEEE Conference on Decision Control . 2005 , Seville, Spain. pp. 4457 – 4462 .
  • Bibian , S and Jin , H . 2000 . Time Delay Compensation of Digital Control for DC Switch Mode Power Supplies using Prediction Techniques . IEEE Transactions on Power Electronics , 15 : 835 – 842 .
  • Da , X , Cheng , C and Tang , B . 2000 . A Linear Matrix Inequality Approach for Robust Control of Systems with Delayed States . European Journal of Operational Research , 124 : 332 – 341 .
  • Franklin , GF , Powell , JD and Emami-Naeini , A . 2002 . Feedback Control of Dynamic Systems , Upper Saddle River, New Jersey : Prentice Hall .
  • Fridman , E and Shaked , U . 2003 . Parameter Dependent Stability and Stabilisation of Uncertain Time-delay Systems . IEEE Transactions on Automatic Control , 48 : 861 – 866 .
  • Han , QL and Gu , KQ . 2001 . On Robust Stability of Time-delay Systems with Norm Bounded Uncertainty . IEEE Transactions on Automatic Control , 46 : 1426 – 1431 .
  • Hassibi , A and Boyd , SP . 1998 . Quadratic Stabilisation and Control of Piecewise-linear Systems . Proceedings of American Control Conference . 1998 , Philadelphia, Pennsylvani. pp. 3659 – 3664 .
  • Johansson , M . 2003 . Piecewise Linear Control Systems , Berlin, Heidelberg : Springer .
  • Kulkarni , V , Jun , M and Hespanha , J . 2004 . Piecewise Quadratic Lyapunov Functions for Piecewise Affine Time-delay Systems . American Control Conference . 2004 , Boston, Massachusetts. pp. 3885 – 3889 .
  • Lin , QWC and Lee , TH . 2006 . A Less Conservative Robust Stability Test for Linear Uncertain Time-delay Systems . IEEE Transactions on Automatic Control , 51 : 87 – 91 .
  • Momeni , A and Aghdam , AG . 2007 . An Adaptive Tracking Problem for a Family of Retarded Time-delay Plants . International Journal of Adaptive Control and Signal Processing , 21 : 885 – 910 .
  • Mondie , S and Kharitonov , V . 2005 . Exponential Estimates for Retarded Time-delay Systems: An LMI Approach . IEEE Transactions on Automatic Control , 50 : 268 – 273 .
  • Parlakci , M . 2006 . Robust Stability of Uncertain Time-varying State-delayed Systems . IEE Proceedings on Control Theory and Applications , 153 : 469 – 477 .
  • Rodrigues , L . 2004 . Stability Analysis of Piecewise-affine Systems using Controlled Invariant Sets . Systems & Control Letters , 53 : 157 – 169 .
  • Rodrigues , L and Boukas , E . 2006 . Piecewise-linear ℋ∞ Controller Synthesis with Applications to Inventory Control of Switched Production Systems . Automatica , 42 : 1245 – 1254 .
  • Rodrigues , L and Boyd , SP . 2005 . Piecewise-affine State Feedback for Piecewise-affine Slab Systems using Convex Optimisation . Systems & Control Letters , 54 : 835 – 583 .
  • Rodrigues , L and How , JP . 2003 . Observer-based Control of Piecewise-affine Systems . International Journal of Control , 76 : 459 – 477 .
  • Rodrigues , L and How , J . 2006 . Toward Unified Analysis and Controller Synthesis for a Class of Hybrid Systems . Nonlinear Analysis , 65 : 2216 – 2235 .
  • Su , JH . 1994 . Further Results on the Robust Stability of Linear Systems with a Single Time Delay . Systems & Control Letters , 23 : 375 – 379 .
  • Sun , XM , Zhao , J and Hill , D . 2006a . Stability and L2-gain Analysis for Switched Delay Systems: A Delay-dependent Method . Automatica , 42 : 1769 – 1774 .
  • Sun , YG , Wong , L and Xie , G . 2006b . Stability of Switched Systems with Time-varying Delays: Delay-dependent Common Lyapunov Functional Approach . Proceedings of American Control Conference . 2006b , Minneapolis, Minnesota. pp. 1544 – 1549 .
  • Tousi , MM , Karuei , I , Hashtrudi-Zad , SH and Aghdam , AG . 2008 . Supervisory Control of Switching Control Systems . Systems & Control Letters , 57 : 132 – 141 .
  • Verriest , EI , Fan , MKH and Kullstam , J . 1993 . Frequency Domain Robust Stability Criteria for Linear Delay Systems . Proceedings of the 32nd IEEE Conference on Decision and Control . 1993 , San Antonio, Texas. pp. 3473 – 3478 .
  • Wang , SS , Chen , BS and Lin , TP . 1987 . Robust Stability of Uncertain Time-delay Systems . International Journal of Control , 46 : 963 – 976 .
  • Wang , Y , Xie , L and de Souza , CE . 1992 . Robust Control of a Class of Uncertain Nonlinear Systems . Systems & Control Letters , 19 : 139 – 149 .
  • Wei , Y , Rodrigues , L and Gordon , B . 2006 . Piecewise-affine Control of a Three DOF Aerobatic Helicopter . Proceedings of American Control Conference . 2006 , Minneapolis, Minnesota. pp. 3924 – 3929 .
  • Zhai , GS , Sun , Y , Chen , XK and Anthony , NM . 2003 . Stability and L2 Gain Analysis for Switched Symmetric Systems with Time Delay . Proceedings of American Control Conference . 2003 , Denver, Colorado. pp. 2682 – 2687 .
  • Zhang , W , Branicky , M and Phillips , SM . 2001 . Stability of Networked Control Systems . IEEE Control Systems Magazine , 21 : 84 – 99 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.