研究会 (2008 年 03 月 11 日)

日時: 3/11(火) 14:00〜18:00

場所: 九州工業大学天神サテライトキャンパス kyutech プラザ

講演: 1. Stability criteria for interconnections of ISS systems
　　     (Dr. Sergey Dashkovskiy, University of Bremen, 14:00〜15:45)
　　  2. Construction of a Lyapunov function for circadian oscillations
         of Drosophila with a new theory of stability analysis
　　     (伊藤博, 九州工業大学, 16:00〜17:45)

参加者: Dr. Dashkovskiy(Univ. of Bremen), 佐藤(佐賀大)
　　　  向井(九大), 伊藤, 瀬部(九工大)

講演概要:

1. We will start with an introduction to the notion of input-to-state
   stability (ISS) accompanied with simple examples. This notion becomes
   very popular for studying nonlinear dynamical systems with inputs.
   We will also provide some remarks on possible variations of this notion.
   An ISS-Lyapunov function for such systems will be also introduced.
   Then we will consider interconnactions of such systems. The main question is:
   whether this stability property is preserved by interconnections. We will
   present stability criteria for an interconnection of ISS systems.
   Morover we will give a constructive approach how a Lyapunov function
   can be found for a given inteconnection.
   In the end we will consider an example of application of our stability
   criterion. This example is related to logistic systems.

2. In this talk, we consider the problem of understanding the dynamics of 
   robustly persistent circadian oscillations in cells of Drosophila. 
   The circadian oscillation has been motivating the speaker to develop 
   mathematical tools to verify stability by means of construction of 
   Lyapunov functions. Recently, he has proposed a new Lyapunov-type 
   methodology for the stability analysis of networks of scalar 
   dissipative systems. This approach contrasts numerical ones which have 
   been dominant in system-theoretic studies of circadian oscillations. 
   Since each scalar variable describing the concentration of a substance 
   naturally involves nonlinear autonomous and interactive dynamics in the 
   network of proteins and mRNA, the dissipativity of each dynamics is 
   asymmetric with respect to the balance point. 
   This talk explains how we are able to make use of asymmetric integral 
   input-to-state stability (asymmetric iISS) characterizations of 
   subsystems in estimating the behavior of the whole network. The 
   Lyapunov-type analytical approach will be illustrated by explicitly 
   constructing a Lyapunov function which determines the necessary ranges 
   of parameters for maintaining oscillations of a circadian model in 
   the cells of Drosophila.