Absolute stability of systems with multiple non-linearities

Abstract

A frequency-domain criterion for the asymptotic stability-in-the-large of systems containing many non-linearities is derived in terms of the positive realness of the product of a diagonal multiplier matrix and the transfer function matrix of the linear part. Several sub-classes of monotonically increasing non-linear functions are considered and it is shown that the elements of the multiplier matrix can be permitted to have complex conjugate poles and zeros whon the non-linearities possess at least a restricted odd asymmetry. A Lyapunov function of the quadratic plus multi integral type and a matrix version of the Meyer-Kalman-Yakubovich lemma are used in deriving the results.