How to Get a Conservative Well-Posed Linear System Out of Thin Air. Part II. Controllability and Stability

Marius Tucsnak, George Weiss
2003 SIAM Journal of Control and Optimization  
The following proposition is a restatement of a part of Theorem I.1.3. Proposition 1.2. With the notation of Theorem 1.1 and (1.7)-(1.10), the semigroup generator of Σ is A, its control operator is B, and its observation operator is and we have G(s) ≤ 1 for all s ∈ C 0 . Now we have all the necessary ingredients to state the new results of this paper. The following theorems use various controllability, observability, and stability concepts. The precise definition of these concepts is given in
more » ... ction 2. Theorem 1.3. With the above notation, the following assertions are equivalent :
doi:10.1137/s0363012901399295 fatcat:mhzovdiiovcftntnm5ymaolnhe