研究会 (2007 年 11 月 12 日)

日時: 11/12(月) 14:00〜18:00

講演概要:

1. Behaviorに基づくシステム理論は，システムを入出力作用素
   としてではなく，システム変数の時間応答軌道の集合(behavior)
   として特徴づけることにより，伝達関数や状態方程式に基づく既
   存のシステム制御理論よりも自然かつ柔軟な理論展開を可能とするもので
   ある．本発表では，まず，behaviorシステム理論の動機付けを行い，
   behaviorに関するいくつかの基礎概念およびbehaviorの解析に有
   用な２次微分形式を導入する．そして，２次微分形式を用いた
   behaviorの安定解析に関する最近の研究成果を紹介する．

2. The notions of input-to-state stability (ISS) and integral input-to-state 
   stability (iISS) have had a great impact on the analysis and synthesis of 
   nonlinear delay-free systems. It is very natural to believe that 
   these concepts will play an important role also in the case of 
   retarded nonlinear systems. In this seminar a general tool, based on 
   Liapunov-Krasovskii functionals, for checking the ISS and the iISS of 
   retarded nonlinear systems is presented. A Liapunov-Krasovskii theorem 
   for an integral input/state estimate which, different from the past 
   literature, takes into account nonzero initial conditions, is presented 
   too. Technical problems, as far as the absolute continuity of the 
   functional evaluated at the solution and the equality of functional 
   derivatives in the time domain and in the state space domain, are shown and 
   solved. First results concerning the input-to-state stabilizability of 
   stabilizable retarded nonlinear systems, affected by disturbances adding 
   to the control law, are shown. An application to the study of the ISS of
   a stirred tank chemical reactor in closed loop with a nonlinear 
   controller is presented and the effectiveness of the previous 
   Liapunov-Krasovskii tool is shown.