研究会 (2014 年 01 月 07 日)

概要

1. Hybrid and impulsive systems combine the continuous dynamics with 
   instantaneous jumps of a state and play a significant role in modern
   control theory. In this talk we will consider recent developments in 
   input-to-state stability (ISS) theory of such systems. We will start with a 
   simpler class of impulsive systems by presenting how Lyapunov methods 
   together with fixed or average dwell-time conditions lead us to criterions, 
   ensuring ISS of impulsive systems. Since the construction of an ISS Lyapunov 
   function for nonlinear systems is a complicated task by itself, we present 
   next a small-gain design of Lyapunov functions for impulsive systems 
   consisting of several components. Then we will switch our attention to 
   hybrid systems. Here we will see, that most of the stability results for 
   impulsive systems can be transferred to hybrid systems. Last but not least 
   we show how the average dwell-time (ADT) clocks and reverse ADT clocks can 
   be used to modify the Lyapunov functions for subsystems and to enlarge the 
   applicability of derived small-gain theorems.

 Speaker's biographcal sketch: 

   Andrii Mironchenko (アンドリ ミロンチェンコ) received his M.Sc. degree in 
   applied mathematics at I.I. Mechnikov Odessa National University, Ukraine in 
   2008 and his Ph.D. degree in mathematics at University of Bremen, Germany in 
   2012. In 2012 he joined the Institute of Mathematics at the University of 
   Wu"rzburg as a research assistant (Postdoc). Currently he is a JSPS 
   Postdoctoral Fellow at Kyushu Institute of Technology, Iizuka, Japan. His 
   research interests include stability theory, distributed parameter systems, 
   and applications of control theory to biological systems. 

2. A method of designing semiglobal and practical discrete-time reduced-order 
   observers for nonlinear sampled-data strict-feedback systems is presented in 
   this talk. Robustness of the designed observers is discussed, which allows 
   us to design of reduced-order observer-based output feedback controllers. 
   Numerical and practical examples are given to show the efficiency of the 
   designed observers and output feedback controllers. 

3. In this talk we consider stability and robustness of nonlinear stochastic 
   dynamical systems. For robustness, both input-to-state noise-to-state 
   properties are discussed for several choices of measures for external 
   signals and noises. The robustness properties are characterized in terms of 
   Lyapunov functions. This talk attempts to focus on how things become 
   different in the presence of stochastic noises. A reasonable Lyapunov-type 
   framework for verifying stability and robustness of interconnected systems 
   will be presented briefly.