Stability analysis of the delayed feedback ccontrol method with commutative gain matrices (original) (raw)
2010
The purpose of our investigation is to guarantee the delayed feedback control method in chaos control proposed by Pyragas analytically. Recently, we gave the conditions for deciding whether the control method is successful under some assumption(we will say “Commutative Assumption”) by using the Floquet theory to a delay differential equation. In this article, we summarize the above results and the fundamental matter of the Floquet theory to a delay differential equation. As an application, we will also show numerically that some unstable periodic orbits of the Rössler system can be stabilized by the method using a different control gain matrix from that which Pyragas used. Especially, the numerical result that the 3 times periodic orbit can be stabilized is newly obtained result.
Related papers
2013
Since modeling of real plants inevitably gives rise to modeling errors regarded as uncertainties, considering robustness for the uncertainties is important in actual control problems. For tackling issues of analyzing robust stability of closed-loop systems in a less conservative fashion, the μ-analysis method is known to be effective. As an alternative approach to robust stability analysis, on the other hand, discrete-time noncausal linear periodically time-varying (LPTV) scaling has been proposed recently. This approach can be naturally introduced through the lifting-based treatment of systems, and the associated conservativeness can be reduced by increasing the period of lifting. This thesis is concerned with this lifting-based scaling approach. In this thesis, we first review the definition and properties of noncausal LPTV scaling. This scaling approach is a generalization of the conventional causal linear time-invariant (LTI) scaling, and coincides with the latter scaling when w...
Loading Preview
Sorry, preview is currently unavailable. You can download the paper by clicking the button above.