A combined frequency-time domain stability criterion for autonomous continuous systems

An improved sufficient condition for asymptotic stability developed for the monotone nonlinearity is Re Z (j) (G (j) + 1/k₂) or Re Z (j, ) (G (j) + 1/k₂) 0 where Z (s) =1++Y (s) and 0|y (t) |dt. Examples of allowed Z (s) functions are considered which show that the angle of G (j) +1/k₂ is permitted to take on both positive and negative values outside the 90 band. The approach used in deriving the above results is a general one which reduces the problem of obtaining sufficient conditions for asymptotic stability to one of obtaining a bound for a cross-correlation function R (T) in terms of R (O). As an example, a sufficient condition for asymptotic stability is developed for a continuous nonlinearity having a monotone bound which appears to have considerable practical application.