Hilbert Space에서 대수 Riccati 방정식으로 얻어지는 교란된 Co-Semigroup의 상한에 대한 연구

A study on upper bounds of the perturbed co-semigroups via the algebraic riccati equation in hilbert space

Upper bounds of the perturbed Co-semigroups of the infinite dimensional systems are investigated by using the algebraic Riccati equation(ARE). In the case that the solution P of the ARE is strictly positive, the perturbed semigroups are uniformly bounded. A sufficient condition for the solution P to be strictly positive is provided. The uniform boundedness plays an important role in extending approximately weak stability to weak stability on th whole space. Exponential Stability of the perturbed semigroups is studied by using the Young's inequlity. Some further discussions on the uniform boundedness of the perturbed semigroups are given.