Qualitative analysis of oscillations in nonlinear control systems: a describing function approach. (English) Zbl 0596.93049
The authors analyse the stability of oscillations for a class of control systems, consisting of a linear part and a nonlinear part connected in a single-loop feedback configuration. They make use of the describing function method and of a result on integral manifolds, together with some technicalities, such as coordinate transformation and averaging. The main result concerns the existence of an integral manifold, whose stability is determined by computable parameters. The results are applied to specific examples.
Reviewer: A.Perdon
MSC:
93D25 | Input-output approaches in control theory |
34C15 | Nonlinear oscillations and coupled oscillators for ordinary differential equations |
93C10 | Nonlinear systems in control theory |
34C29 | Averaging method for ordinary differential equations |
34C45 | Invariant manifolds for ordinary differential equations |