Linear and bilinear infinite-dimensional representations of finite-dimensional non-linear systems

DOI10.1080/00207728508926717zbMath0577.93007OpenAlexW1988083120MaRDI QIDQ3699523

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Publication date: 1985

Published in: International Journal of Systems Science (Search for Journal in Brave)

Full work available at URL: http://eprints.whiterose.ac.uk/76802/1/report%20259.pdf

zbMATH Keywords

tensorial formulationCarleman transformationnonlinear analytic control systems

Mathematics Subject Classification ID

Nonlinear systems in control theory (93C10) Transformations (93B17) Algebraic methods (93B25) Existence theories for optimal control problems involving ordinary differential equations (49J15) General theory of linear operators (47A99) Multilinear algebra, tensor calculus (15A69)

Related Items (6)

\(H_ \infty\) control design in bilinear systems: A tensor formal series approach ⋮ Tensor operators and limit cycles in non-linear systems ⋮ On the equivalent bilinearization of non-linear controlled delay systems ⋮ Algebraic condition for observability of non-linear analytic systems ⋮ Functional expansion and stability for non-linear input-output maps ⋮ On the optimal control of nonlinear systems

Cites Work

• On a class of suboptimal controls for infinite-dimensional bilinear systems
• Transformation of a nonlinear system into an augmented linear system
• Global implicit function theorems
• Global transformations of nonlinear systems
• Describing functions revisited
• On the generation of infinite-dimensional bilinear systems and Volterra series
• Justification of the Describing Function Method
• On the Equivalence of Control Systems and the Linearization of Nonlinear Systems

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