Marchenko, V. M.; Asmykovich, I. K. On the qualitative control theory in dynamic systems with distributed delay. (English) Zbl 0562.93050 Control of distributed parameter systems, Proc. 3rd IFAC Symp., Toulouse 1982, 181-188 (1983). Summary: [For the entire collection see Zbl 0559.00028.] The paper deals with the problems of controllability and observability of delay-differential systems which directly generalize the corresponding problems for ordinary linear dynamic systems without delay. We introduce a number of definitions which define more exactly a notion of the state for hereditary systems as the minimal part of data needed for generating a unique trajectory of the system. We also introduce a notion of informator for the characterization of states and generalize the well- known Lagrange’s identity to systems with delay. This result is used for the investigation of some controllability problems of delay functional systems. Dual results and the problem of computation of the minimum number of outputs needed for \(\infty\)-observability of the system is also presented. MSC: 93C35 Multivariable systems, multidimensional control systems 34K35 Control problems for functional-differential equations 93B05 Controllability 49N15 Duality theory (optimization) 93B07 Observability 93C05 Linear systems in control theory Keywords:controllability and observability; delay-differential systems; Dual results Citations:Zbl 0559.00028 PDFBibTeX XML