Localization and parametrization of linear multidimensional control systems

DOI10.1016/S0167-6911(99)00030-4zbMath0948.93016OpenAlexW2090180537MaRDI QIDQ1960463

Jean-François Pommaret, Alban Quadrat

Publication date: 12 January 2000

Published in: Systems \& Control Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0167-6911(99)00030-4

zbMATH Keywords

controllabilitytransfer matrixminimal realizationdifferential modulelocalizationformal integrabilityhomological algebracontroller formparametrization of differential operators

Mathematics Subject Classification ID

Algebraic methods (93B25) Realizations from input-output data (93B15) Other classes of modules and ideals in associative algebras (16D80)

Related Items

Algebraic Theory of Linear Systems: A Survey ⋮ Recent progress in an algebraic analysis approach to linear systems ⋮ Relative parametrization of linear multidimensional systems ⋮ A differential operator approach to multidimensional optimal control ⋮ Parametrization of Cosserat equations ⋮ On necessary and sufficient conditions for differential flatness ⋮ Serre's reduction of linear partial differential systems with holonomic adjoints ⋮ Unnamed Item ⋮ On the computation of \(\pi\)-flat outputs for linear time-varying differential-delay systems ⋮ Factoring and decomposing a class of linear functional systems ⋮ Computation of bases of free modules over the Weyl algebras. ⋮ Effective algorithms for parametrizing linear control systems over Ore algebras ⋮ Unnamed Item ⋮ Time-autonomy versus time-controllability ⋮ A search for positive storage functions ⋮ An algebraic interpretation to the operator-theoretic approach to stabilizability. I: SISO systems ⋮ Conditions for time-controllability of behaviours

Cites Work

• Multidimensional constant linear systems
• Algebraic theory for multivariable linear systems
• Some basic structural properties of generalized linear systems
• Generalized Bézout identity.
• Continuous time-varying linear systems
• Transfer operators and state spaces for discrete multidimensional linear systems
• An algebraic interpretation of the Laplace transform and of transfer matrices
• Primeness of multivariate polynomial matrices
• A formal theory of matrix primeness
• The Quillen - Suslin theorem and the structure of n-dimensional elementary polynomial matrices
• Notes on n-Dimensional System Theory
• Controllability and observability of linear delay systems: an algebraic approach
• Algebraic study of systems of partial differential equations
• Algebraic analysis of linear multidimensional control systems
• Prolongations of linear partial differential equations. I. A conjecture of Élie Cartan
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item