This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
R.A. ADAMS, Sobolev spaces, Academic Press, New York 1975.
V. BARBU and S.I. GROSSMAN, Asymptotic behavior of linear integrodifferential systems, Trans. Amer. Math. Soc. 173 (1972), 277–288.
J.G. BORISOVIC and A.S. TRBABIN, On the Cauchy problem for linear non-homogeneous differential equations with retarded argument, Solviet Math. Doklady 10 (1969), 401–405.
J.A. BURNS and T.L. HERDMAN, Adjoint semigroup theory for a Volterra integrodifferential system, Bulletin of the American Mathematical Society 81 (1975), 1099–1102.
, Adjoint semigroup theory for a class of functional differential equations, SIAM J. Math. Anal. 7 (1976), 729–745.
J.A. BURNS, T.L. HERDMAN and H.W. STECH, The Cauchy problem for linear functional differential equations, Conference on Integral and Functional Differential Equations, Morgantown, West Virginia, June 1979.
R. DATKO, Extending a theorem of A.M. Liapunov to Hilbert space, J. Math. Anal. Appl. 32 (1970), 610–616.
, Neutral Autonomous Functional Equations with Quadratic Cost, SIAM J. Control 12 (1974), 70–82.
[3], Differential-difference equations in Hilbert spaces, in "Proc. 14th Annual Allerton Conference on Circuit and System Theory, U. of Illinois at Urbana-Champaign", pp. 62–69, October 1976.
, Representation of solutions and stability of linear differential-difference equations in a Banach space, J. Differential Equations 29 (1978), 105–166.
M.C. DELFOUR, The largest class of hereditary systems defining a C0 semigroup on the product space, Canadian J. of Mathematics 32 (1980), to appear.
, Numerical solution of the operator Riccati equation for the filtering of linear stochastic hereditary differential systems, in "Optimization techniques, modelling and optimization in the service of man", Part 2, J. Cea, ed., pp. 700–719, Springer-Verlag, New York 1976.
, The linear quadratic optimal control problem for hereditary differential systems: theory and numerical solution, J. Applied Mathematics and Optimization, 3 (1977), 101–162.
M.C. DELFOUR, E.B. LEE and A. MANITIUS, F-reduction of the operator Riccati equation for hereditary differential systems, Automatica 14 (1978), 385–395.
M.C. DELFOUR, C. McCALLA and S.K. MITTER, Stability and the infinite-time quadratic cost problem for linear hereditary differential systems, SIAM J. Control 13 (1975), 48–88.
M.C. DELFOUR and A. MANITIUS, The structural operator F and its role in the theory of retarded systems I, J. Math. Anal. Appl. 73 (1980), 466–490.
The structural operator F and its role in the theory of retarded systems II, J. Math. Anal. Appl. 74 (1980).
M.C. DELFOUR and S.K. MITTER, Controllability, observability and optimal feedback control of affine hereditary differential systems, SIAM J. Control 10 (1972), 298–328.
O. DIEKMANN, Volterra integral equations and semigroups of operators, Report TW 197/80, Stichting Mathematisch Centrum, January 1980, Amsterdam.
J.K. HALE, Linear functional-differential equations with constant coefficients, Contributions to Differential Equations 2 (1963), 291–319.
, Functional differential equations, Springer-Verlag, New York, 1971.
, Theory of functional differential equations, Springer-Verlag, New York, 1977.
D. HENRY, Linear autonomous neutral functional differential equations, J. Differential Equations 15 (1974), 106–128.
A. ICHIKAWA, Generation of a semigroup on some product space with applications to evolution equations with delay, Control theory centre report no. 52, University of Warwick, Coventry.
, Optimal quadratic control and filtering for evolution equations with delay in control and observation, Control theory centre no. 53, University of Warwick, Coventry, June 1977.
H. KOIVO and E.B. LEE, Controller synthesis for linear systems with retarded state and control variables and quadratic cost, Automatica 8 (1972), 203–208.
R.H. KWONG, A linear-quadratic Gaussian theory for systems with delays in the state, control and observations, Report 7714, Systems Control Group, University of Toronto, Canada, September 1977.
The linear quadratic Gaussian problem for systems with delays in the state, control, and observation, Proc. 14th Allerton conference on circuit and system theory, pp. 545–549, University of Illinois, 1976.
, A stability theory of the Linear-Quadratic-Gaussian problem for systems with delays in the state, control, and observations, SIAM J. Control and Optimization 18 (1980), 49–75.
R. KWONG and A.S. WILLSKY, Optimal filtering and filter stability of linear stochastic delay systems, IEEE Trans. Automatic Control AC-22 (1977), 196–201.
, Estimation and filter stability of stochastic delay systems, SIAM J. Control and Optimization 16 (1978), 660–681.
A. MANITIUS, Controllability, observability and stabilizability of retarded systems, Proc. 1976 IEEE Conference on Decision and Control, pp. 752–758, IEEE Publications, New York, 1976.
, Completeness and F-completeness of eigenfunctions associated with retarded functional differential equations, J. Differential Equations 35 (1980), 1–29, to appear.
Necessary and sufficient conditions of approximate controllability for general linear retarded systems, Report CRMA-898, University of Montreal, September 1979.
These proceedings.
A. MANITIUS and A.W. OLBROT, Finite spectrum assignment problem for systems with delays, IEEE Trans. on Automatic Control AC-24 (1979).
A. MANITIUS and R. TRIGGIANI, Function space controllability of linear retarded systems: a derivation from abstract operator conditions, SIAM J. Control and Optimization 16 (1978).
R.K. MILLER, Linear Volterra integrodifferential equations as semigroups, Funkcial. Ekvac 17 (1974), 39–55.
S.K. MITTER and R. VINTER, Filtering for linear stochastic hereditary differential systems, in "Control theory, numerical methods and computer systems modelling", A. Bensoussan and J.L. Lions, eds., pp. 1–21, Springer-Verlag, New York, 1975.
A.W. OLBROT, Stabilizability, detectability, and spectrum assignment for linear autonomous systems with general time delays, IEEE Trans. on Automatic Control AC-23 (1978), 887–890.
J.-Y. OUVRARD, Projection de martingale et filtrage linéaire dans des espaces de Hilbert (part I), et, Un exemple d'application au problème de lissage pour les systèmes héréditaires (part II), Mémoire principal de soutenance, U. Scientifique et Médicale de Grenoble, septembre 1977.
Martingales et filtrage linéaire dans des espaces Hilbertiens — théorie du lissage pour des systèmes héréditaires, Thèse de doctorat, U. Scientifique et Médicale de Grenoble, septembre 1977.
L. PANDOLFI, Canonical realizations of systems with delayed controls, Ricerche di Automatica 10 (1979), 27–37.
, On feedback stabilization of functional differential equations, Bolletino U.M.I. 4, 11, Supplemento al fascicolo 3, Giugno 1975, Serie VI VI, Vol. XI, 626–635
D. SALAMON, On finite dimensional perturbation of semigroups corresponding to differential delay systems, Report 14, FS Dynamische Systeme, Universität Bremen, May 1980.
Some properties of semigroups in IRn×Lp corresponding to delay systems, Report 18, FS Dynamische Systeme, Universität Bremen, May 1980.
R.B. VINTER, On a problem of Zabczyk concerning semigroups generated by operators with non-local boundary conditions, Publication 77/8 (1977), Department of Computing and Control, Imperial College of Science and Technology, London (England).
, Semigroups on product spaces with applications to initial value problems with non-local boundary conditions, in "Control of distributed parameter systems", S.P. Banks and A.J. Pritchard, eds., pp. 91–98, Pergamon Press, Oxford, England 1978.
A representation of solutions to stochastic delay equations, Appl. Math. and Optimization, to appear.
, Filter stability for stochastic evolution equations, SIAM J. on Control and Optimization 15 (1977), 465–485.
R.B. VINTER and R.H. KWONG, The infinite time quadratic control problem for linear systems with state and control delays: an evolution equation approach, SIAM J. on Control and Optimization, to appear.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1980 Springer-Veralg
About this paper
Cite this paper
Delfour, M.C. (1980). Status of the state space theory of linear hereditary differential systems with delays in state and control variables. In: Bensoussan, A., Lions, J.L. (eds) Analysis and Optimization of Systems. Lecture Notes in Control and Information Sciences, vol 28. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0004035
Download citation
DOI: https://doi.org/10.1007/BFb0004035
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-10472-8
Online ISBN: 978-3-540-38489-2
eBook Packages: Springer Book Archive