非局所境界条件に無駄時間を含む1階双曲型システムに対するオブザーバ

誤差システムのL²-安定性

抄録

This note is concerned with the problem of designing observers for a first-order hyperbolic system that has a time lag in the nonlocal boundary condition. In our previous work, an infinite-dimensional observer could be constructed for the system by using a backstepping approach, and it was shown that the classical solution of the error system could be finite-time stabilized. In this note, we focus on the L²-stability of the error system and prove that the operator describing the error system generates a nilpotent semigroup on the augmented L²-space. As a result, the function space to which the initial value of the error system belongs is enlarged.