Byrnes, C.; Hu, X.; Martin, C. F.; Shubov, V. Input-output behavior for stable linear systems. (English) Zbl 0982.93067 J. Franklin Inst. 338, No. 4, 497-507 (2001). The authors consider a controllable, observable, asymptotically stable, single-input single-output finite-dimensional linear system. In particular, they consider the input-output problem in a fairly general class of Hilbert space. The problem in this generality appears to be very difficult, but they determine a large class of Hilbert spaces for which the result is true and give a series of counterexamples to the more obvious conjectures. Reviewer: Park Jong Yeoul (Pusan) MSC: 93D25 Input-output approaches in control theory 93C25 Control/observation systems in abstract spaces 93C05 Linear systems in control theory Keywords:stability; input-output stability; linear system; input-output problem; Hilbert space PDFBibTeX XMLCite \textit{C. Byrnes} et al., J. Franklin Inst. 338, No. 4, 497--507 (2001; Zbl 0982.93067) Full Text: DOI References: [1] Kailath, T., Linear Systems (1980), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · Zbl 0458.93025 [2] C.T. Chen, Linear System Theory and Design, HRW, 1984.; C.T. Chen, Linear System Theory and Design, HRW, 1984. [3] Silverman, L.; Anderson, B. D.O., Controllability, observability and stability of linear systems, SIAM J. Control, 6, 121-130 (1968) · Zbl 0157.15803 [4] Khalil, H. K., Nonlinear Systems (1996), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · Zbl 0626.34052 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.