Multidimensional constant linear systems

Oberst, Ulrich

doi:10.1007/bfb0021005

Cited by 36 publications

(52 citation statements)

References 31 publications

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“…If = -n (orn × B ) and < is a term order, this can be done by computing a Gröbner basis of W . This was first observed and applied by U. Oberst in [4]. The case = 9 n was treated in [11] and in [10].…”

Section: Contradictionmentioning

confidence: 94%

Gröbner Bases for Ideals in Laurent Polynomial Rings and their Application to Systems of Difference Equations

Pauer¹,

Unterkircher²

1999

Applicable Algebra in Engineering, Communication and Computing

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Abstract. We develop a basic theory of Gröbner bases for ideals in the algebra of Laurent polynomials (and, more generally, in its monomial subalgebras). For this we have to generalize the notion of term order. The theory is applied to systems of linear partial difference equations (with constant coefficients) on 9 n . Furthermore, we present a method to compute the intersection of an ideal in the algebra of Laurent polynomials with the subalgebra of all polynomials.

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Section: Contradictionmentioning

confidence: 94%

Gröbner Bases for Ideals in Laurent Polynomial Rings and their Application to Systems of Difference Equations

Pauer¹,

Unterkircher²

1999

Applicable Algebra in Engineering, Communication and Computing

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“…w = M(d/dx) }, is called an image representation of B and we write B = im(M). It was shown in [5] that there is a one-to-one correspondence between linear differential nD behaviors and submodules of D q . This one-to-one correspondence is valid for the choices…”

Section: Implementabilitymentioning

confidence: 99%

On the regular implementability of nD systems

Trentelman

Napp

2007

Systems & Control Letters

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“…We now discuss two of the important mathematical facts concerned with the above representation, the elimination theorem and the module behavior correspondence [6] which form fundamental pillars of the behavioral theory. As observed in the above model the matrices of representation (3) are deÿned over the polynomial ring R[ ].…”

Section: Fundamental Theoremsmentioning

confidence: 99%

“…We shall again omit the proof which can be developed from the discrete time results of [6]. Using these we can compute the kernel representation of the behavior of W (k) with the help of following lemma.…”

Section: Fundamental Theoremsmentioning

confidence: 99%

A behavioral approach to the control of discrete linear repetitive processes

Sule

Rogers

2004

Systems & Control Letters

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This paper formulates the theory of linear discrete time repetitive processes in the setting of behavioral systems theory. A behavioral, latent variable model for repetitive processes is developed and for the physically deÿned inputs and outputs as manifest variables, a kernel representation of their behavior is determined. Conditions for external stability and controllability of the behavior are then obtained. A su cient condition for stabilizability is also developed for the behavior and it is shown under a mild restriction that, whenever the repetitive system is stabilizable, a regular constant output feedback stabilizing controller exists. Next, a notion of eigenvalues is deÿned for the repetitive process under an action of a closed-loop controller. It is then shown how under controllability of the original repetitive process, an arbitrary assignment of eigenvalues for the closed-loop response can be achieved by a constant gain output feedback controller under the above restriction. These results on the existence of constant gain output feedback controllers are among the most striking properties enjoyed by repetitive systems, discovered in this paper. Results of this paper utilize the behavioral model of the repetitive process which is an analogue of the 1D equivalent model of the dynamics studied in earlier work on these processes.

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Multidimensional constant linear systems

Cited by 36 publications

References 31 publications

Gröbner Bases for Ideals in Laurent Polynomial Rings and their Application to Systems of Difference Equations

Gröbner Bases for Ideals in Laurent Polynomial Rings and their Application to Systems of Difference Equations

On the regular implementability of nD systems

A behavioral approach to the control of discrete linear repetitive processes

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