Relaxed Lyapunov criteria for robust global stabilisation of non-linear systems

References

• Antonelli , R and Astolfi , A . 2000 . ‘Nonlinear Controller Design for Robust Stabilization of Continuous Biological Reactors’ . Proceedings of the IEEE Conference on Control Applications . September 2000 , Anchorage, AL.
   Google Scholar
• Artstein , Z . 1983 . Stabilization with Relaxed Controls . Nonlinear Analysis: Theory, Methods and Applications , 7 : 1163 – 1173 .
   Web of Science ®Google Scholar
• Bailey , JE and Ollis , DF . 1986 . Biochemical Engineering Fundamentals , 2nd , New York : McGraw-Hill .
   Google Scholar
• Clarke , FH , Ledyaev , YS , Sontag , ED and Subbotin , AI . 1997 . Asymptotic Controllability Implies Feedback Stabilization . IEEE Transactions on Automatic Control , 42 : 1394 – 1407 .
   Web of Science ®Google Scholar
• Clarke , FH , Ledyaev , YS , Stern , RJ and Wolenski , PR . 1998 . Nonsmooth Analysis and Control Theory , New York : Springer-Verlag .
   Google Scholar
• De Leenheer , P and Smith , HL . 2003 . Feedback Control for Chemostat Models . Journal of Mathematical Biology , 46 : 48 – 70 .
   PubMed Web of Science ®Google Scholar
• Fillipov , AV . 1988 . Differential Equations with Discontinuous Right-Hand Sides , Dordrecht : Kluwer Academic Publishers .
   Google Scholar
• Freedman , HI , So , JWH and Waltman , P . 1989 . ‘Chemostat Competition with Time Delays’ . IMACS Annals On Computation and Applied Mathematics , 5 ( 1/4 ) : 171 – 173 . 12th IMACS World Congress On Scientific Computation, Paris, July 1988
   Google Scholar
• Freeman , RA and Kokotovic , PV . 1996 . Robust Nonlinear Control Design–State Space and Lyapunov Techniques , Boston : Birkhauser .
   Google Scholar
• Gouze , JL and Robledo , G . 2006 . Robust Control for an Uncertain Chemostat Model . International Journal of Robust and Nonlinear Control , 16 : 133 – 155 .
   Web of Science ®Google Scholar
• Harmard , J , Rapaport , A and Mazenc , F . 2006 . Output Tracking of Continuous Bioreactors Through Recirculation and By-pass . Automatica , 42 : 1025 – 1032 .
   Web of Science ®Google Scholar
• Karafyllis , I and Kravaris , C . 2005 . Robust Output Feedback Stabilization and Nonlinear Observer Design . Systems and Control Letters , 54 : 925 – 938 .
   Web of Science ®Google Scholar
• Karafyllis , I , Kravaris , C , Syrou , L and Lyberatos , G . 2008 . A Vector Lyapunov Function Characterization of Input-to-State Stability with Application to Robust Global Stabilization of the Chemostat . European Journal of Control , 14 : 47 – 61 .
   Web of Science ®Google Scholar
• Khalil , HK . 1996 . Nonlinear Systems , 2nd , Upper Saddle River, NJ : Prentice-Hall .
   Google Scholar
• Ledyaev , YS and Sontag , ED . 1999 . A Lyapunov Characterization of Robust Stabilization . Nonlinear Analysis, Theory, Methods and Applications , 37 : 813 – 840 .
   Web of Science ®Google Scholar
• Lin , Y , Sontag , ED and Wang , Y . 1996 . A Smooth Converse Lyapunov Theorem for Robust Stability . SIAM Journal on Control and Optimization , 34 : 124 – 160 .
   Web of Science ®Google Scholar
• Mailleret , L and Bernard , O . ‘A Simple Robust Controller to Stabilize an Anaerobic Digestion Process’ . Proceedings of the 8th Conference on Computer Applications in Biotechnology . 2001 . pp. 213 – 218 .
   Google Scholar
• Mazenc , F and Bowong , S . 2004 . Backstepping with Bounded Feedbacks for Time-Varying Systems . SIAM Journal Control and Optimization , 43 : 856 – 871 .
   Web of Science ®Google Scholar
• Mazenc , F and Iggidr , A . 2004 . Backstepping with Bounded Feedbacks . Systems and Control Letters , 51 : 235 – 245 .
   Web of Science ®Google Scholar
• Mazenc , F , Malisoff , M and De Leenheer , P . 2007 . On the Stability of Periodic Solutions in the Perturbed Chemostat . Mathematical Biosciences and Engineering , 4 : 319 – 338 .
   PubMed Web of Science ®Google Scholar
• Mazenc , F , Malisoff , M and Harmand , J . 2007 . ‘Stabilization and Robustness Analysis for a Chemostat Model with Two Species and Monod Growth Rates via a Lyapunov Approach’ . Proceedings of the 46th IEEE Conference on Decision and Control . 2007 , New Orleans.
   Google Scholar
• Mazenc , F , Malisoff , M and Harmand , J . 2008 . Further Results on Stabilization of Periodic Trajectories for a Chemostat with Two Species . IEEE Transactions on Automatic Control , 53 : 66 – 74 .
   Web of Science ®Google Scholar
• Mazenc , F and Praly , L . 1996 . Adding Integrations, Saturated Controls and Stabilization for Feedforward Systems . IEEE Transactions on Automatic Control , 41 : 1559 – 1578 .
   Web of Science ®Google Scholar
• Smith , H and Waltman , P . 1995 . “ ‘The Theory of the Chemostat. Dynamics of Microbial Competition’ ” . In Cambridge Studies in Mathematical Biology , Vol. 13 , Cambridge : Cambridge University Press .
   Google Scholar
• Sontag , ED . 1989 . A “Universal” Construction of Artstein's Theorem on Nonlinear Stabilization . Systems and Control Letters , 13 : 117 – 123 .
   Web of Science ®Google Scholar
• Sontag , ED . 1998 . Mathematical Control Theory , 2nd , New York : Springer-Verlag .
   Google Scholar
• Sontag , ED . 2003 . A Remark on the Converging-Input Converging-State Property . IEEE Transactions on Automatic Control , 48 : 313 – 314 .
   Web of Science ®Google Scholar
• Stuart , AM and Humphries , AR . 1998 . Dynamical Systems and Numerical Analysis , Cambridge : Cambridge University Press .
   Google Scholar
• Sussmann , HJ , Sontag , ED and Yang , Y . 1994 . A General Result on the Stabilization of Linear Systems Using Bounded Controls . IEEE Transactions on Automatic Control , 39 : 2411 – 2425 .
   Web of Science ®Google Scholar
• Teel , AR . 1992 . Global Stabilization and Restricted Tracking for Multiple Integrators with Bounded Controls . Systems and Control Letters , 18 : 165 – 171 .
   Web of Science ®Google Scholar
• Teel , AR . 1996 . On L 2 Performance Induced by Feedbacks with Multiple Saturations . ESAIM Control, Optimisation and Calculus of Variations , 1 : 225 – 240 .
   Google Scholar
• Temam , R . 1998 . Infinite-Dimensional Dynamical Systems in Mechanics and Physics , 2nd , New York : Springer-Verlag .
   Google Scholar
• Tsinias , J . 1997 . Input to State Stability Properties of Nonlinear Systems and Applications to Bounded Feedback Stabilization Using Saturation . ESAIM Control, Optimisation and Calculus of Variations , 2 : 57 – 85 .
   Google Scholar
• Wang , L and Wolkowicz , G . 2006 . A Delayed Chemostat Model with General Nonmonotone Response Functions and Differential Removal Rates . Journal of Mathematical Analysis and Applications , 321 : 452 – 468 .
   Web of Science ®Google Scholar
• Wolkowicz , G and Xia , H . 1997 . Global Asymptotic Behavior of a Chemostat Model with Discrete Delays . SIAM Journal on Applied Mathematics , 57 : 1019 – 1043 .
   Web of Science ®Google Scholar
• Zhu , L and Huang , X . 2006 . Multiple Limit Cycles in a Continuous Culture Vessel with Variable Yield . Nonlinear Analysis , 64 : 887 – 894 .
   Web of Science ®Google Scholar
• Zhu , L , Huang , X and Su , H . 2007 . Bifurcation for a Functional Yield Chemostat When One Competitor Produces a Toxin . Journal of Mathematical Analysis and Applications , 329 : 891 – 903 .
   Web of Science ®Google Scholar