The Nullstellensatz for systems of PDE

DOI10.1006/aama.1999.0657zbMath0939.35012OpenAlexW2160720998MaRDI QIDQ1961907

Shiva Shankar

Publication date: 19 June 2000

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/aama.1999.0657

zbMATH Keywords

controllable behaviorWillems module

Mathematics Subject Classification ID

Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Polynomials in real and complex fields: location of zeros (algebraic theorems) (12D10)

Related Items (12)

Linear-quadratic control and quadratic differential forms for multidimensional behaviors ⋮ Interconnections of \(\mathcal{L}^2\)-behaviors: lumped systems ⋮ A real nullstellensatz for free modules ⋮ Making waves ⋮ A nullstellensatz for linear partial differential equations with polynomial coefficients ⋮ On restrictions of \(n\)-d systems to 1-d subspaces ⋮ Checking dissipativity of linear behavior systems given in kernel representation ⋮ Linear systems, and ARMA- and Fliess models ⋮ Algebraic characterization of approximate controllability of behaviours of spatially invariant systems ⋮ Regular implementation in the space of compactly supported functions ⋮ Lyapunov stability ofn-D strongly autonomous systems ⋮ Key problems in the extension of module-behaviour duality

Cites Work

• Multidimensional constant linear systems
• Can one control the vibrations of a drum?
• Paradigms and puzzles in the theory of dynamical systems
• A Behavioral Approach to Control of Distributed Systems
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