Singular perturbations, averaging and other time scaled methods


Singular perturbations, averaging and methods for analysis of slowly varying systems can all be referred to as "time-scaled methods" for analysis of dynamical systems that have a two time scale property, where some variables evolve much faster or slower than the rest of the system. Classical results on these methods are presented for systems without disturbances and we have extended them for a range of stability proeprties of systems without disturbances. We obtained a unified approach for analysis of input-to-state stability and other stability properties of two time scale systems with inputs whose special cases are classical results on singular perturbations, averaging and slowly varying systems without inputs. We have applied these results to pulse width modulated control of systems with disturbances.


  • Prof. A.R. Teel
  • Dr. D. Angeli
  • Dr. P.M. Dower
  • Dr. L. Moreau
  • Selected publications

  • A.R. Teel, L. Moreau and D. Nesic, "A unification of time-scale methods for systems with disturbances", IEEE Trans. Automat. Contr, vol.48 (2003), pp. 1526-1544.
  • D. Nesic and A.R.Teel, "Input-to-state stability for nonlinear time-varying systems via averaging", Math. Contr. Sign. Syst. (MCSS), vol.14 (2001), pp. 257-280.
  • A. R. Teel and D. Nesic, "Averaging with disturbances and closeness of solutions", Sys. Contr. Lett, vol. 40, No. 5 (2000), pp. 317-323.
  • D. Nesic and P.M. Dower, "A note on input to state stability and averaging of systems with inputs", IEEE Trans. Automat. Contr., vol. 46, No. 11 (2001), pp. 1760-1765.
  • D. Angeli and D. Nesic, "A trajectory based approach for stability robustness of systems with inputs", Math. Contr. Sign. Syst. (MCSS),vol. 15 (2001) pp. 336-355.
  • A.R.Teel, L.Moreau and D.Nesic, "Input-to-state set stability of pulse width modulated controllers with disturbances", Systems and Control Letters, vol. 51 (2004), pp. 23-32.