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- Eva Zerz, Vakhtang Lomadze
- SIAM J. Control and Optimization
- 2001

By a multidimensional behavior, we mean the solution space of a linear constant-coefficient system of partial difference or differential equations. Within the behavioral framework, a natural concept… (More)

- Vakhtang Lomadze
- 2007

It is shown that a linear differentiation-invariant subspace of a C∞-trajectory space is differential (i.e., can be represented as the kernel of a linear constant-coefficient differential operator)… (More)

Abstract paper concerns with linear systems having arbitrary singularity at infinity. These systems deserve to study since they are limits of familiar classical linear systems. An axiomatic… (More)

- Vakhtang Lomadze
- MCSS
- 2001

Abstract. A linear behavior is defined essentially as a family of finite but sufficiently long trajectories that is invariant with respect to restriction operators. This may be singular in the sense… (More)

- Vakhtang Lomadze
- Int. J. Control
- 2009

The set of classical AR-models is not ‘compact’, so that a sequence of AR-models may fail to converge to anything reasonable. A compactification leads to AR-models with arbitrary singularity at… (More)

- Vakhtang Lomadze
- 2006

We give a necessary and sufficient condition for a subsystem of a plant to be a regular feedback interconnection of an admissible controller with the plant. We also parameterize the set of… (More)

- Vakhtang Lomadze
- 2004

Abstract In this paper we provide a simple version of Oberst's duality between finitely generated polynomial modules and the solution sets of partial differential (and difference) equations.

- Vakhtang Lomadze
- 2002

As is known, the notion of homotopy equivalence is a fundamental notion of mathematics and was introduced in order to formalize a relation that is weaker than isomorphism. In this note we define a… (More)

- Vakhtang Lomadze
- Systems & Control Letters
- 2014

Abstract We show that a set of smooth trajectories is the solution set of a linear constant coefficient partial differential equation if and only if it is linear, shift-invariant and complete. (By… (More)

The notion of behaviors introduced by Willems gives a good description of dynamicalsystems without reference to any particular representation of the system in terms of equations. Inthis note, we… (More)