Stability regions of discrete linear periodic systems with delayed feedback controls

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.Dohan Kim was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean Government (MSIT) (No. 2018R1D1A1B07041273 and No. 2021R1A2C1092945

The complete chloroplast genome sequence of Abies nephrolepis (Pinaceae: Abietoideae)

AbstractThe plant chloroplast (cp) genome has maintained a relatively conserved structure and gene content throughout evolution. Cp genome sequences have been used widely for resolving evolutionary and phylogenetic issues at various taxonomic levels of plants. Here, we report the complete cp genome of Abies nephrolepis. The A. nephrolepis cp genome is 121,336 base pairs (bp) in length including a pair of short inverted repeat regions (IRa and IRb) of 139 bp each separated by a small single copy (SSC) region of 54,323 bp (SSC) and a large single copy region of 66,735 bp (LSC). It contains 114 genes, 68 of which are protein coding genes, 35 tRNA and four rRNA genes, six open reading frames, and one pseudogene. Seventeen repeat units and 64 simple sequence repeats (SSR) have been detected in A. nephrolepis cp genome. Large IR sequences locate in 42-kb inversion points (1186 bp). The A. nephrolepis cp genome is identical to Abies koreana’s which is closely related to taxa. Pairwise comparison between two cp genomes revealed 140 polymorphic sites in each. Complete cp genome sequence of A. nephrolepis has a significant potential to provide information on the evolutionary pattern of Abietoideae and valuable data for development of DNA markers for easy identification and classification