Estimates of the transient response of Lur´e-type systems

The problem of estimating the extreme time constants associated with the transient response of a Lur´e-type nonlinear system is considered. This problem has been discussed in the recent past by Vogt,1 who showed that bounds for these time constants can be obtained from a knowledge of the eigenvalues of the linear part of the system. The object of the present study has been to improve upon this result, by including the effects of the nonlinear part. The proposed method is believed to be quite simple and is illustrated with the help of numerical examples.