Print Email Facebook Twitter Null controllability and the algebraic Riccati equation in Banach Spaces Title Null controllability and the algebraic Riccati equation in Banach Spaces Author Van Neerven, J.M.A.M. Faculty Electrical Engineering, Mathematics and Computer Science Department Delft Institute of Applied Mathematics Date 2005-01-05 Abstract By a recent result of Priola and Zabczyk, a null controllable linear system [y'(t) = Ay(t) + Bu(t)] in a Hilbert space E is null controllable with vanishing energy if and only if it is null controllable and the only positive self-adjoint solution of the associated algebraic Riccati equation [XA + A* X - XBB* X = 0] is the trivial solution X = 0. In this paper we extend this result to Banach spaces with an elementary proof which uses only reproducing kernel Hilbert space techniques. We also show that null controllability with vanishing energy implies null controllability Subject null controllability with vanishing energyalgebraic Riccati equationreproducing kernel Hilbert space To reference this document use: http://resolver.tudelft.nl/uuid:bcc144e6-528b-4bf0-954e-9e921c84aaef Publisher Society for Industrial and Applied Mathematics, SIAM Source SIAM Journal on Control and Optimization, 43 (4), 2005 Part of collection Institutional Repository Document type journal article Rights (c) 2005 Society for Industrial and Applied Mathematics /islandora/object/uuid:bcc144e6-528b-4bf0-954e-9e921c84aaef/datastream/OBJ/view