Admissibility of Unbounded Control Operators

Tangential Interpolation in Weighted Vector-valued Hp Spaces, with Applications

“…Admissibility implies that the mild solution of (17) corresponding to an initial condition x(0) = x 0 ∈ H and to u ∈ U is a continuous H-valued function of t. The case U = L p (0, ∞; C N ) has been introduced and studied in [18] and [17]. The case U = H 2 β (R + ) seems to be new and not yet studied in the literature.…”

“…This can then be solved using the results of Section 2. Using (18), it follows that the system (17) is exactly controllable if and only if ℓ s (N) ⊆ BU . where B : U → {x : N → C} is defined by (19).…”

Quadratic optimal control of stable well-posed linear systems

“…By a result due to Salamon [35] (and apparently discovered independently by Weiss [43,44]), every well-posed linear system Ψ has a well-defined (unbounded) control operator B and a well-defined (unbounded) observation operator C, and formulas (3), (4), (8), (9), (11), (12), (13), and (15) hold in a weak sense (see Remark 30 below). In order to present this result we need some additional definitions.…”

“…This theory has been developed in [33], [34], [35], [8], [11], and [43], [44], [45], [46] (and many other papers), and we refer the reader to these sources for additional reading. (Salamon calls these systems "well-posed semigroup control systems" and Weiss calls them "abstract linear systems".)…”

New Riccati equations for well-posed linear systems

“…We say that A, B, C, D are the generating operators of the well-posed linear system. In fact, any well-posed linear system has uniquely defined generating operators A, B, C where A is the infinitesimal generator of the strongly continuous semigroup A and B and C are in general unbounded operators (see Weiss [15], [16]). In general a feedthrough operator 'D' may not exist.…”