Function Space Controllability of Linear Retarded Systems: A Derivation from Abstract Operator Conditions

Manitius, A.; Triggiani, Roberto

doi:10.1137/0316041

Cited by 126 publications

(49 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…For retarded functional differential equations (FDE's), extensive studies of controllability were done in the space W2 (l) [2] and R n × L2([ -h,0], R") [19,20]. In each case, controllability in the full state space was proven to be quite a restrictive concept, imposing quite severe conditions on system matrices.…”

Section: Introductionmentioning

confidence: 99%

F-controllability and observability of linear retarded systems

Manitius

1982

Appl Math Optim

Self Cite

View full text Add to dashboard Cite

Abstract. The paper gives new results on F-controllability of linear retarded functional differential equations. The concept of F-controllability, weaker than the approximate controllability in the state space, has been introduced by this author in 1976. In the present paper new conditions are presented which, in the case of systems with one delay, become easily verifiable criteria of F-controllability. A duality between F-controllability and observability is discussed, and several examples are given.

show abstract

Section: Introductionmentioning

confidence: 99%

F-controllability and observability of linear retarded systems

Manitius

1982

Appl Math Optim

Self Cite

View full text Add to dashboard Cite

show abstract

“…We shall now state conditions which guarantee approximate controllability of (6.4). In terms of the original system (6.1)-(6.2), this is called function-space controllability: see [10,11,13]. We use Theorem 4.6: to be precise, the equivalence of (a) and (c).…”

Section: Thenmentioning

confidence: 99%

Semigroup Theory for Control on Sun-reflexive Banach Spaces

Heijmans¹

1987

IMA J Math Control Info

View full text Add to dashboard Cite

show abstract

“…The properties of stabilizability and detectability, and their relationships to controllability and observability, are further discussed in [18], [25], [26], to which the reader is referred.…”

Section: (T) -A'y(t)-b'y(t +Z)-c'u(t)mentioning

confidence: 99%

Estimation and Filter Stability of Stochastic Delay Systems

Kwong¹,

Willsky²

1978

SIAM J. Control Optim.

View full text Add to dashboard Cite

Abstract. Linear and nonlinear filtering for stochastic delay systems are studied. A representation theorem for conditional moment functionals is obtained, which, in turn, is used to derive stochastic differential equations describing the optimal linear or nonlinear filter. A complete characterization of the optimal filter is given for linear systems with Gaussian noises. Stability of the optimal filter is studied in the case where there are no delays in the observations. Using the duality between linear filtering and control, asymptotic stability of the optimal filter is proved. Finally, the cascade of the optimal filter and the deterministic optimal quadratic control system is shown to be asymptotically stable as well.

show abstract

Function Space Controllability of Linear Retarded Systems: A Derivation from Abstract Operator Conditions

Cited by 126 publications

References 32 publications

F-controllability and observability of linear retarded systems

F-controllability and observability of linear retarded systems

Semigroup Theory for Control on Sun-reflexive Banach Spaces

Estimation and Filter Stability of Stochastic Delay Systems

Contact Info

Product

Resources

About