A Design of Delayed Feedback via Sampled-Data H_∞ Control

Abstract

A design problem of DFC (delayed feedback control) satisfying H_∞ performance specification is considered for sampled-data systems. It is shown that stabilization of UPOs (unstable periodic orbits) can be cast into an H_∞ control synthesis with an unstable weight. The nonstandard synthesis problem is then reduced to a standard one under mild condition, which also concludes that the DFC structure is necessary for the stabilization of UPOs. A synthesis problem is formulated by putting extra sampled-data H_∞ specifications to the problem related to the stabilization of UPOs, and the properties including the order of the resultant controller are discussed. The validity of the proposed method is confirmed by numerical examples.