Kappel, Franz; Salamon, Dietmar An approximation theorem for the algebraic Riccati equation. (English) Zbl 0717.49030 SIAM J. Control Optimization 28, No. 5, 1136-1147 (1990). Summary: For an infinite-dimensional linear quadratic control problem in Hilbert space, approximation of the solution of the algebraic Riccati operator equation in the strong operator topology is considered under conditions weaker than uniform exponential stability of the approximating systems. As an application, strong convergence of the approximating Riccati operators in case of a previously developed spline approximation scheme for delay systems [see the authors, ibid. 27, No.2, 407-431 (1989; Zbl 0695.93047); ibid. 25, 1082-1117 (1987; Zbl 0642.34065)] is established. Finally, convergence of the transfer-functions of the approximating systems is investigated. Cited in 12 Documents MSC: 49N10 Linear-quadratic optimal control problems 93D15 Stabilization of systems by feedback 41A15 Spline approximation 93B40 Computational methods in systems theory (MSC2010) 34K35 Control problems for functional-differential equations Keywords:hereditary control systems; infinite-dimensional linear quadratic control problem in Hilbert space; algebraic Riccati operator; approximating Riccati operators; spline approximation; delay systems Citations:Zbl 0695.93047; Zbl 0642.34065 PDFBibTeX XMLCite \textit{F. Kappel} and \textit{D. Salamon}, SIAM J. Control Optim. 28, No. 5, 1136--1147 (1990; Zbl 0717.49030) Full Text: DOI