240
Views
21
CrossRef citations to date
0
Altmetric
Original Articles

Global uniform asymptotical stability of a class of nonlinear cascaded systems with application to a nonholonomic wheeled mobile robot

, &
Pages 1301-1312 | Received 26 Dec 2007, Accepted 24 Feb 2009, Published online: 30 Sep 2010

References

  • Arcak , M , Angeli , D and Sontag , E . 2002 . A Unifying Integral ISS Framework for Stability of Nonlinear Cascadeds . SIAM Journal on Control and Optimization , 40 : 1888 – 1904 .
  • Astolfi , A . 1996 . Discontinuous Control of Nonholonomic Systems . System and Control Letters , 27 : 37 – 45 .
  • Bhat , SP and Bernstein , DS . 1997 . Finite-time Stability of Homogeneous Systems . Proceedings of the American control conference . 1997 . pp. 1073 – 1078 . Albuquerque, , New Mexico
  • Bhat , SP and Bernstein , DS . 2005 . Geometric Homogeneity with Applications to Finite-time Stability . Mathematics of Control, Signals and Systems , 17 : 101 – 127 .
  • Chaillet , A and Angeli , D . 2008 . Integral Input to State Stable Systems in Cascade . Systems and Control Letters , 57 : 519 – 527 .
  • Dixon , WE , Dawson , DM , Zergeroglu , E and Behal , A . 2001 . Nonlinear Control of Wheeled Mobile Robots , London : Springer .
  • Haimo , VT . 1986 . Finite-time Controllers . SIAM Journal on Control and Optimization , 24 : 760 – 770 .
  • Hermes , H . 1991 . Homogeneous Coordinates and Continuous Asymptotically Stabilising Feedback Controls . Differential Equations, Stability and Control , 109 : 249 – 260 .
  • Hespanha , JP and Morse , AS . 1999 . Stabilization of Nonholonomic Integrators via Logic-based Switching . Automatica , 35 : 385 – 393 .
  • Imura , JI , Sugie , T and Yoshikawa , T . 1994 . Global Robust Stabilization of Nonlinear Cascaded Systems . IEEE Transactions on Automatic Control , 39 : 1084 – 1089 .
  • Hong , Y . 2002 . Finite-time Stabilization and Stabilizability of a Class of Controllable Systems . Systems and Control Letters , 46 : 231 – 236 .
  • Hong , Y , Huang , J and Xu , Y . 2001 . On an Output Feedback Finite-time Stabilization Problem . IEEE Transactions on Automatic Control , 46 : 305 – 309 .
  • Hong , Y , Xu , Y and Huang , J . 2002 . Finite Time Control for Robot Manipulators . Systems and Control Letters , 46 : 243 – 253 .
  • Jankovic , M , Sepulchre , R and Kokotovic , PV . 1996 . Constructive Lyapunov Stabilization of Nonlinear Cascade Systems . IEEE Transactions on Automatic Control , 41 : 1723 – 1735 .
  • Jiang , ZP . 1999 . A Recursive Technique for Tracking Control of Nonholonomic Systems in Chained Form . IEEE Transactions on Automatic Control , 44 : 265 – 279 .
  • Jiang , ZP and Nijmeijer , H . 1997 . Tracking Control of Mobile Robots: A Case Study in Backstepping . Automatica , 33 : 1393 – 1399 .
  • Kanayama , Y . ‘A stable tracking control method for an autonomous mobile robot’, in Proceedings of IEEE International Conference on Robotica and Automation, Cincinnati, OH, 1990, pp. 384-389
  • Kawski , M . 1990 . Homogeneous Stabilizing Feedback Laws . Control Theory and Advanced Technology , 6 : 497C516
  • Kawski , M . 1995 . Geometric Homogeneity and Applications to Stabilization . Proceedings of 3rd IFAC symposium on nonlinear control systems . 1995 . pp. 164 – 169 . Lake Tahoe, CA
  • Kurzweil , J . 1956 . On the Inversion of Lyapunov's Second Theorem on Stability of Motion . American Mathematical Society Translations , 24 : 19 – 77 .
  • Li , S and Tian , Y . 2007 . Finite-time Stability of Cascaded Time-varying Systems . International Journal of Control , 80 : 646 – 657 .
  • Lozano , R , Brogliato , B and Landau , ID . 1992 . Passivity and Global Stabilization of Cascaded Nonlinear Systems . IEEE Transactions on Automatic Control , 37 : 1386 – 1389 .
  • Orlov , Y . 2003 . Finite Time Stability of Homogeneous Switched Systems . Proceedings of the 42nd IEEE Conference on Decision and Control . 2003 . pp. 4271 – 4276 . Hawaii
  • Ortega , R . 1991 . Passivity Properties for Stabilization of Nonlinear Cascaded Systems . Automatica , 27 : 423 – 424 .
  • Panteley , E and Loria , A . 1998a . On Global Uniform Asymptotic Stability of Nonlinear Time-varying Systems in Cascade . Systems and Control Letters , 33 : 131 – 138 .
  • Panteley , E and Loria , A . 1998b . “ Exponential Tracking of a Mobile Car using a Cascaded Approach ” . In IFAC Workshop on Motion Control 221 – 226 . Grenoble, , France
  • Panteley , E and Loria , A . 2001 . Growth Rate Conditions for Uniform Asymptotic Stability of Cascaded Time-varying Systems . Automatica , 37 : 453 – 460 .
  • Panteley , E , Loria , A and Sokolov , A . 1999 . Global Uniform Asymptotic Stability of Cascaded Non-autonomous Non-linear Systems: Application to Stabilization of a Diesel Engine . European Journal of Control , 5 : 107 – 115 .
  • Qian , CJ and Lin , W . 2006 . Recursive Observer Design, Homogeneous Approximation, and Nonsmooth Output Feedback Stabilization of Nonlinear Systems . IEEE Transactions on Automatic Control , 51 : 1457 – 1471 .
  • Rosier , L . 1992 . Homogeneous Lyapunov Function for Homogeneous Continuous Vector Field . Systems and Control Letters , 19 : 467 – 473 .
  • Rui , C and McClamroch , NH . 1995 . Stabilization and Asymptotic Path Tracking of a Rolling Disk . Proceedings of 34th IEEE Conference on Decision and Control . 1995 . pp. 4294 – 4299 . New Orleans
  • Saberi , A , Kokotovic , PV and Sussmann , HJ . 1990 . Global Stabilization of Partially Linear Composite System . SIAM Journal on Control and Optimization , 28 : 1491 – 1503 .
  • Samson , C . 1990 . “ Velocity and Torque Feedback Control a Nonholonomic Cart ” . In International Workshop on Adaptive and Nonlinear Control 125 – 151 . Grenoble
  • Samson , C . 1995 . Control of Chained Systems: Application to Path Following and Time-varying Point-stabilization of Mobile Robots . IEEE Transactions on Automatic Control , 40 : 64 – 77 .
  • Samson , C and Ait-abderrahim , K . 1991 . Feedback Control of a Nonholonomic Wheeled Cart in Cartesian Space . Proceedings of the IEEE International Conference on Robotics and Automation . 1991 . pp. 1136 – 1141 . Sacramento
  • Sepulchre , R , Arcak , M and Teel , AR . 2002 . Trading the Stability of Finite Zeros for Global Stabilization of Nonlinear Cascade Systems . IEEE Transactions on Automatic Control , 47 : 521 – 525 .
  • Sepulchre , R , Jankovic , M and Kokotovic , P . 1996 . Constructive Nonlinear Control , London : Springer .
  • Seibert , P and Suarez , R . 1990 . Global Stabilisation of Nonlinear Cascaded Systems . Systems and Control Letters , 14 : 347 – 352 .
  • Shih , C and Jeng , J . 1999 . Stabilization of Non-holonomic Chained Systems by Gain Scheduling . International Journal of Systems Science , 30 : 441 – 449 .
  • Sontag , E . 1989a . Smooth Stabilization Implies Coprime Factorization . IEEE Transactions on Automatic Control , 34 : 435 – 443 .
  • Sontag , E . 1989b . Remarks on Stabilization and Input-to State Stability . Proceedings of 28th IEEE Conference on Decision and Control . 1989b . pp. 1376 – 1378 . Tampa
  • Sontag , E . 1990 . Further Facts About Input to State Stabilisation . IEEE Transactions on Automatic Control , 35 : 473 – 446 .
  • Tian , Y and Li , S . 2002 . Exponential Stabilization of Nonholonomic Dynamic Systems by Smooth Time-varying Feedback . Automatica , 38 : 1139 – 1146 .
  • Vidysagar , M . 1980 . Decomposition Techniques for Large-scale Systems with Nonadditive Interactions: Stability and Stabilisability . IEEE Transactions on Automatic Control , 25 : 773 – 779 .
  • Wang , Z , Li , S and Fei , S . 2009 . Finite-tIme Tracking Control of a Nonholonomic Mobile Robot . Asian Journal of Control , 11 : 344 – 357 .
  • Xu , J , Pan , Y , Lee , T and Fridman , L . 2005 . On Nonlinear H ∞ Sliding Mode Control for a Class of Nonlinear Cascaded Systems . International Journal of Systems Science , 36 : 983 – 992 .
  • Yoshizawa , T . 1975 . Stability Theory and the Existence of Periodic Solutions and Almost Periodic Solutions , New York : Springer .

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.