This paper focuses on Forced oscillations (periodic and almost periodic) in some dynamical models described by coupled differential and difference equations. The existence and stability result is based on a theorem on invariant manifolds on Banach spaces due to Kurzweil and Halanay. The state‐space (based on Liapunov–Krasovskii functionals combined with the S‐procedure) approach is considered. An illustrative example is presented and some conclusions are drawn concerning sharpness and ease in applications of the method.

This paper deals with the exponential stability analysis of switched neutral systems under certain state-dependent switching rules with nonlinear perturbations bounded in magnitude. The proposal of an energy functional allow us to investigate the asymptotic and exponential stability of switched neutral systems through the solution of linear matrix inequalities. The results are illustrated with the exponential stability analysis of an oilwell drilling system allowing a significant reduction of the stick slip behavior.

Feedback systems with several differentiable non-linearities are considered. For the absolute stability problem a frequency domain criterion is obtained incorporating only slope information about non-linearities and containing a multiplier of the form P + (iω)^-1Q, where P and Q are diagonal matrices. For the case of a single non-linearity, connections with similar results of other authors are discussed.