Geometric criterion for the design of a non-oscillatory dynamical system

The paper deals with responses of a non-linear multiple lumped dynamical system bounded in a large neighbourhood of the single, asymptotically stable equilibrium point. The sufficient, analytic criteria for the non-oscillation of such responses have been introduced in previous work (cf. Skowronaki and Shannon 1972). On the basis of the latter, the author discusses a geometric interpretation of necessary and sufficient criteria for non-oscillatory responses applied to the synthetic design of the relevant systems

Conditions for non-oscillatory response of multiple non-linear systems

A dynamical system is modelled by the non-linear equation: x¨+F(x, ẋ) = 0, where F is an analytic function denned on some open domain δ phase-space E2nAssuming the ultimate boundedness of responses in the arbitrarily largo bounded neighbourhood δHδ of an asymptotically stable single singular point, the conditions for non-oscillatory approach of responses to that point are considered. The design of the system to achieve this property is proposed, proving that linear criteria may be employed