The use of finite-dimensional linear time-invariant controllers for the stabilization of periodic solutions in sinusoidally forced nonlinear systems is investigated. By mixing results concerning absolute stability of nonlinear systems and robustness of linear systems, a linear matrix inequality-based controller synthesis technique is developed. The synthesis algorithm yields the controller maxi...

An asymptotically stable direct adaptive fuzzy PI sliding mode controller is proposed for a class of nonlinear uncertain systems. In contrast to other existing approaches of handling disturbances, the proposed approach does not require this bound to be known, only requiring that it exists. Moreover, a PI control structure is used to attenuate chattering. The approach is applied to stabilize an ...

We prove that when subjected to periodic forcing of the form pμ,ρ,ω(t) = μ(ρh(x, y) + sin(ωt)), certain 2-dimensional vector fields with dissipative homoclinic loops admit strange attractors with SRB measures for a set of forcing parameters (μ, ρ, ω) of positive Lebesgue measure. The proof extends ideas of Afraimovich and Shilnikov [1] and applies the recent theory of rank 1 maps developed by W...

The bistablity onset due to the interaction of highto low-frequency oscillations in the Duffing oscillator is considered. It is shown that such interaction results in arising of additional bistable states, which has a lower threshold for bistability with respect to the forcing amplitude as compared to the harmonically forced oscillator. This phenomenon is illustrated by considering two examples...

By using a generalization of the multiple scales technique we develop a method to derive amplitude equations for zero-dimensional forced systems. The method allows to consider either additive or multiplicative forcing terms and can be straightforwardly applied to the case that the forcing is white noise. We give examples of the use of this method to the case of the van der Pol-Duffing oscillato...