A general realization theory for higher-order linear differential equations

Ravi, M.S.; Rosenthal, Joachim

doi:10.1016/0167-6911(94)00085-a

Cited by 30 publications

(11 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Note also that the systems of the form (2.4) modulo state space equivalence can be naturally identified with a Zariski open subset of a (projective) variety, a so called Quot Scheme. (See [24,27,28]). This gives an alternative way to speak about a generic set of linear systems.…”

Section: We Would Like To Remark That If I Is the Ideal Generated Bymentioning

confidence: 99%

Inverse Eigenvalue Problems for Multivariable Linear Systems

Rosenthal

Wang

1997

Systems and Control in the Twenty-First Century

Self Cite

View full text Add to dashboard Cite

Section: We Would Like To Remark That If I Is the Ideal Generated Bymentioning

confidence: 99%

Inverse Eigenvalue Problems for Multivariable Linear Systems

Rosenthal

Wang

1997

Systems and Control in the Twenty-First Century

Self Cite

View full text Add to dashboard Cite

“…One motivation for the author to take a module-theoretic approach to convolutional coding theory has come from algebraic-geometric considerations. As is explained in [31,39,40], a submodule of rank k and degree δ in F n [z] describes a quotient sheaf of rank k and degree δ over the projective line P 1 . The set of all such quotient sheaves having rank k and degree at most δ has the structure of a smooth projective variety denoted by X δ k,n .…”

Section: Some Geometric Remarksmentioning

confidence: 99%

Connections Between Linear Systems and Convolutional Codes

Rosenthal¹

2001

Codes, Systems, and Graphical Models

View full text Add to dashboard Cite

The article reviews different definitions for a convolutional code which can be found in the literature. The algebraic differences between the definitions are worked out in detail. It is shown that bi-infinite support systems are dual to finite-support systems under Pontryagin duality. In this duality the dual of a controllable system is observable and vice versa. Uncontrollability can occur only if there are bi-infinite support trajectories in the behavior, so finite and half-infinite-support systems must be controllable. Unobservability can occur only if there are finite support trajectories in the behavior, so bi-infinite and half-infinite-support systems must be observable. It is shown that the different definitions for convolutional codes are equivalent if one restricts attention to controllable and observable codes.

show abstract

“…In this way we make the connection with work of Hinrichsen and O'Halloran [9]. Following the exposition in [10,16] consider (n + p) × n matrices K, L and a (n + p) × (m + p) matrix M. Those matrices define a generalized state space system through…”

Section: Resultsmentioning

confidence: 99%

Output feedback invariants

Ravi

Rosenthal

Helmke

2002

Linear Algebra and its Applications

Self Cite

View full text Add to dashboard Cite

The paper is concerned with the problem of determining a complete set of invariants for output feedback. Using tools from geometric invariant theory it is shown that there exists a quasi-projective variety whose points parameterize the output feedback orbits in a unique way. If the McMillan degree n ≥ mp, the product of number of inputs and number of outputs, then it is shown that in the closure of every feedback orbit there is exactly one nondegenerate system. * The main results of this paper were announced

show abstract

A general realization theory for higher-order linear differential equations

Cited by 30 publications

References 7 publications

Inverse Eigenvalue Problems for Multivariable Linear Systems

Inverse Eigenvalue Problems for Multivariable Linear Systems

Connections Between Linear Systems and Convolutional Codes

Output feedback invariants

Contact Info

Product

Resources

About