Stability regions of discrete linear periodic systems with delayed feedback controls

Abstract

We propose a geometric method to determine the stability region of the zero solution of a linear periodic difference equation via the delayed feedback control (briefly, DFC) with the commuting feedback gain. For the equation, our method is more effective than the Jury criterion. First, we give a relationship, named the C-map theorem, between the characteristic multipliers of an original equation and those of the equation via DFC. Next, we show the existence and m-starlike property, defined in this paper, of an m-closed curve induced from the C-map. Using this result, we prove that the region enclosed by the m-closed curve is the stability region of the zero solution of the equation via DFC.