Construction of ISS interval observers for triangular systems

We consider classes of nonlinear block triangular systems, for which we design interval observers. They possess the well known robustness property of Input to State Stability with respect to the bounds of the time varying disturbances. The systems under study are in general not cooperative and not globally Lipschitz. We illustrate the constructions by two bioreactors models, the first one dealing with competition of two bacterial species and the second one representing a cascade of anaerobic bioreactions.

[1]  S. Sastry.  Nonlinear Systems: Analysis, Stability, and Control , 1999 .

[2]  Paul Waltman,et al.  The Theory of the Chemostat , 1995 .

[3]  Eduardo Sontag.  Smooth stabilization implies coprime factorization , 1989, IEEE Transactions on Automatic Control.

[4]  O. Bernard,et al.  INTERVAL OBSERVERS FOR NON MONOTONE SYSTEMS. APPLICATION TO BIOPROCESS MODELS , 2005 .

[5]  David Angeli,et al.  A characterization of integral input-to-state stability , 2000, IEEE Trans. Autom. Control..

[6]  A. Vande Wouwer,et al.  Improving continuous–discrete interval observers with application to microalgae-based bioprocesses , 2009 .

[7]  A Genovesi,et al.  Dynamical model development and parameter identification for an anaerobic wastewater treatment process. , 2001, Biotechnology and bioengineering.

[8]  Olivier Bernard,et al.  Asymptotically Stable Interval Observers for Planar Systems With Complex Poles , 2010, IEEE Transactions on Automatic Control.

[9]  Jean-Luc Gouzé,et al.  Closed loop observers bundle for uncertain biotechnological models , 2004 .

[10]  Y. Candau,et al.  Bounded error moving horizon state estimator for non-linear continuous-time systems: application to a bioprocess system , 2005 .

[11]  Michael Malisoff,et al.  Review of Lyapunov Functions , 2009 .

[12]  Jean-Luc Gouzé,et al.  Near optimal interval observers bundle for uncertain bioreactors , 2007 .

[13]  David Angeli,et al.  A Unifying Integral ISS Framework for Stability of Nonlinear Cascades , 2001, SIAM J. Control. Optim..

[14]  Olivier Bernard,et al.  Robust interval observers for global Lipschitz uncertain chaotic systems , 2010, Syst. Control. Lett..

[15]  J. Gouzé,et al.  Interval observers for uncertain biological systems , 2000 .

[16]  M. Malisoff,et al.  Constructions of Strict Lyapunov Functions , 2009 .

[17]  Olivier Bernard,et al.  Exponentially Stable Interval Observers for Linear Systems with Delay , 2012, SIAM J. Control. Optim..

[18]  Olivier Bernard,et al.  Interval observers for linear time-invariant systems with disturbances , 2011, Autom..