Globally uniformly asymptotical stabilisation of time-delay nonlinear systems

References

• Cai , X and Han , Z . 2006a . An Analysis and Design Method for Systems with Structural Uncertainty . International Journal of Control , 79 : 1647 – 1653 .
   Web of Science ®Google Scholar
• Cai , X and Han , Z . 2006b . Universal Construction of Control Lyapunov Functions for Linear Systems . Latin American Applied Research , 36 : 15 – 22 .
   Google Scholar
• Cao , Y , Lin , Z and Hu , T . 2002 . Stability Analysis of Linear Time-delay Systems Subject to Input Saturation . Systems and Control Letters , 49 : 233 – 240 .
   Google Scholar
• El Houssaine , T . 2007 . Delay-dependent Robust Stability of Linear Systems with Non-commensurate Time Varying Delays . International Journal of Systems Science , 38 : 749 – 757 .
   Google Scholar
• Freeman , R and Kokotovic , P . 1996 . Robust Nonlinear Control Design , Boston : Birkhauser .
   Google Scholar
• Freeman , R and Praly , L . 1998 . Integrator Backstepping for Bounded Controls and Control Rates . IEEE Transactions on Automatic Control , 43 : 258 – 262 .
   Google Scholar
• Grovlen , A . and Fossen, T. (1996), ‘Nonlinear Control of Dynamic Positioned Ships Using Only Position Feedback: an Observer Backstepping Approach’, in Proceedings of the 35th IEEE Conference on Decision and Control, Kobe, Japan, pp. 3388–3393.
   Google Scholar
• Gu , K , Kharitonov , V and Chen , J . 2003 . Stability of Time-delay Systems , Boston : Birkhauser .
   Google Scholar
• Gwang-Seok , P , Ho-Lim , C and Jong-Tae , L . 2008 . On Stability of Linear Time-delay Systems with Multiple Delays . International Journal of Systems Science , 39 : 839 – 852 .
   Google Scholar
• Isidori , A . 1996 . Global Almost Disturbance Decoupling with Stability for Non-minimum-phase Single-input Single-output Nonlinear Systems . Systems and Control Letters , 28 : 115 – 122 .
   Google Scholar
• Jankovic , M . 2001 . Control Lyapunov–Razumikhin Functions and Robust Stabilization of Time Delay Systems . IEEE Transactions on Automatic Control , 46 : 1048 – 1060 .
   Web of Science ®Google Scholar
• Jiang , Z and Nijmeijer , H . 1997 . Tracking Control of Mobile Robots: A Case Study in Backstepping . Automatica , 33 : 1393 – 1399 .
   Web of Science ®Google Scholar
• Jiang , Z , Teel , AR and Praly , L . 1994 . Small-gain Theorem for ISS Systems and Applications . Mathematics of Control, Signals, and Systems , 7 : 95 – 120 .
   Web of Science ®Google Scholar
• Jun , Y and Takuo , T . 2008 . New Delay-dependent Conditions on Robust Stability and Stabilisation for Discrete-time Systems with Time-delay . International Journal of Systems Science , 39 : 1033 – 1040 .
   Google Scholar
• Kokotovic , P and Arcak , M . 2001 . Constructive Nonlinear Control: A Historical Perspective . Automatica , 37 : 637 – 662 .
   Web of Science ®Google Scholar
• Krstic , M and Deng , H . 1998 . Stabilization of Nonlinear Uncertain Systems , New York : Springer .
   Google Scholar
• Krstic , M , Kanellakopoulos , I and Kokotovic , P . 1995 . Nonlinear and Adaptive Control Design , New York : Wiley .
   Google Scholar
• Lebel , S . and Rodrigues, L. (2007), ‘Path Following of a Wheeled Mobile Robot Combining Piecewise-affine Synthesis and Backstepping Approaches’, in Proceedings of the American Control Conference, New York, pp. 4518–4523.
   Google Scholar
• Marino , R and Tomei , P . 1993 . Robust Stabilization of Feedback Linearizable Time-varying Uncertain Systems . Automatica , 29 : 181 – 189 .
   Web of Science ®Google Scholar
• Mazenc , F . 2004 . Backstepping with Bounded Feedbacks . Systems and Control Letters , 51 : 235 – 245 .
   Web of Science ®Google Scholar
• Mazenc , F and Bliman , P . 2006 . Backstepping Design for Time-delay Nonlinear System . IEEE Transactions on Automatic Control , 51 : 149 – 154 .
   Web of Science ®Google Scholar
• Mazenc , F , Mondie , S and Franciso , R . 2003 . Global Asymptotic Stabilization for Chains of Integrators with a Delay in the Input . IEEE Transactions on Automatic Control , 48 : 57 – 63 .
   Web of Science ®Google Scholar
• Michiels , W , Sepulchre , R and Roose , D . 2002 . Stability of Perturbed Delay Differential Equations and Stabilization of Nonlinear Cascade Systems . SIAM Journal of Control and Optimization , 40 : 661 – 680 .
   Google Scholar
• Moulay , E and Perruquetti , W . 2005 . Stabilization of Nonaffine Systems: A Constructive Method for Polynomial Systems . IEEE Transactions on Automatic Control , 50 : 520 – 526 .
   Google Scholar
• Oppenheimer , M . Ngo, A., and Blake, W. (2007), ‘Analysis of the Reconfigurable Control Capabilities of a Space Access Vehicle’, in IEEE Aerospace Conference Proceedings, Montana, USA, Big Sky, MT, USA, 3–10 March 2007, 2641–2650.
   Google Scholar
• Pan , Z and Basar , T . 1999 . Backstepping Controller Design for Nonlinear Stochastic Systems Under a Risk-sensitive Cost Criterion . SIAM Journal of Control and Optimization , 37 : 957 – 995 .
   Web of Science ®Google Scholar
• Praly , L and Jiang , Z . 1993 . Stabilization by Output-feedback for Systems with ISS Inverse Dynamics . Systems and Control Letters , 21 : 19 – 33 .
   Web of Science ®Google Scholar
• Teel , A . 1998 . Connections Between Razumikhin-type Theorems and the ISS Nonlinear Small Gain Theorems . IEEE Transactions on Automatic Control , 43 : 960 – 964 .
   Web of Science ®Google Scholar
• Xu , S and Lam , J . 2003 . Survey of Linear Matrix Inequality Techniques in Stability Analysis of Delay Systems . International Journal of Systems Science , 39 : 1095 – 1113 .
   Google Scholar
• Zhang , Y , Fidan , B and Ioannou , P . 2003 . Control of Linear Time-varying Systems with Known and Unknown Parameters . IEEE Transactions on Automatic Control , 48 : 1908 – 1926 .
   Web of Science ®Google Scholar