The structural operator F and its role in the theory of retarded systems. II

DOI10.1016/0022-247X(80)90134-1zbMath0464.34050MaRDI QIDQ1154038

Andrzej Manitius, Michel C. Delfour

Publication date: 1980

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

Hilbert spaceF-completenesscanonical spectral projectionsfinite-dimensional spectral projections

Mathematics Subject Classification ID

Groups and semigroups of linear operators (47D03) Functional-differential equations (including equations with delayed, advanced or state-dependent argument) (34K99)

Related Items (15)

State space theory of linear time invariant systems with delays in state, control, and observation variables. I, II ⋮ Pointwise completeness and degeneracy of functional differential equations in Banach spaces. I: General time delays ⋮ Finite-dimensional regulators for a class of infinite-dimensional systems ⋮ Sobolev space estimates for solutions of equations with delay, and the basis of divided differences ⋮ Series expansions and small solutions for Volterra equations of convolution type ⋮ Unnamed Item ⋮ Functional-differential equations in Sobolev spaces and related problems of spectral theory ⋮ Hautus type controllability conditions by control constraints for distributed systems ⋮ Completeness and F-completeness of eigenfunctions associated with retarded functional differential equations ⋮ Structure theory and duality for the time varying retarded functional differential equations ⋮ A unified approach to constrained approximate controllability for the heat equations and the retarded equations ⋮ Optimality for periodic control of functional differential systems ⋮ Linear optimal control of systems with state and control variable delays ⋮ A sharp version of Henry's theorem on small solutions ⋮ Exact observability and controllability for linear neutral type systems

Cites Work

• Projection series for retarded functional differential equations with applications to optimal control problems
• On degeneracy of functional-differential equations
• Completeness and F-completeness of eigenfunctions associated with retarded functional differential equations
• A folk theorem in functional differential equations
• Small solutions of linear autonomous functional differential equations
• Function Space Controllability of Linear Retarded Systems: A Derivation from Abstract Operator Conditions
• Hereditary Control Problems: Numerical Methods Based on Averaging Approximations
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