An operator theory of linear functional differential equations

Abstract An operator theory, based on convolution rings and modules, is developed for various classes of first-order vector functional differential equations of the retarded type with finite and infinite delays. The existence and construction of complete solutions is approached in a novel manner by incorporating initial data into the operator framework. Results are then obtained on exponential and asymptotic stability. The operator framework is also applied to the study of state feedback. Constructive results on spectrum assignability and stabilizability by feedback are given.

[1]  Michel C. Delfour,et al.  Hereditary Differential Systems with Constant Delays. I. General Case , 1972 .

[2]  L. Schwartz.  Théorie des distributions , 1966 .

[3]  J. A. Burns,et al.  An Abstract Framework for Approximate Solutions to Optimal Control Problems Governed by Hereditary Systems , 1975 .

[4]  J. Hale.  Functional Differential Equations , 1971 .

[5]  Harvey Thomas Banks,et al.  Application of abstract variational theory to hereditary systems--A survey , 1974 .

[6]  Edward W. Kamen,et al.  Representation and realization of operational differential equations with time-varying coefficients , 1976 .

[7]  Michel C. Delfour,et al.  State theory of linear hereditary differential systems , 1977 .

[8]  Michel C. Delfour,et al.  Controllability, Observability and Optimal Feedback Control of Affine Hereditary Differential Systems , 1972 .

[9]  R. Triggiani,et al.  Function Space Controllability of Linear Retarded Systems: A Derivation from Abstract Operator Conditions , 1978 .

[10]  J. A. Burns,et al.  Adjoint Semigroup Theory for a Class of Functional Differential Equations , 1976 .

[11]  J. Hale,et al.  Stability of functional differential equations of neutral type , 1970 .

[12]  Jack K. Hale,et al.  Functional differential equations with infinite delays , 1974 .

[13]  W. D. Evans,et al.  PARTIAL DIFFERENTIAL EQUATIONS , 1941 .

[14]  A. Stephen Morse.  Ring models for delay-differential systems , 1976, Autom..

[15]  Eduardo Sontag.  Linear Systems over Commutative Rings. A Survey , 1976 .

[16]  Michel C. Delfour,et al.  Hereditary differential systems with constant delays. II. A class of affine systems and the adjoint problem , 1975 .