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Stability and Control of Systems with Propagation

  • Vladimir RăsvanEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 94)

Abstract

A natural way of introducing time delay equations is to consider boundary value problems for hyperbolic partial differential equations (PDEs) in two variables. Such problems account for the so-called propagation phenomena that may be found in several physical and engineering applications. Association of some functional (differential/integral) equations to the aforementioned boundary value problems represents a way of tackling basic theory (existence, uniqueness, data dependence, i.e. well posedness) but also some qualitative properties arising from ODEs (ordinary differential equations) such as stability, oscillations, dissipativeness, Perron condition, and others. On the other hand automatic feedback control for systems described by partial differential equations (PDEs), systems called also with distributed parameters, is often ensured by boundary control: the control signals appear as forcing signals at the boundaries. In control applications stability of the feedback structure is the very first requirement. In order to achieve stability, Lyapunov functionals are considered aiming to obtain simultaneously the control structure and stability of the controlled system.

Keywords

Hyperbolic partial differential equations Derivative boundary conditions Equations with deviated arguments Hamilton variational principle Energy identity Lyapunov energy functional Feedback stabilization 

Notes

Acknowledgements

This paper is dedicated to Professor István Győri, outstanding scholar, at his 70th birthday. The work was supported by the project CNCS-Romania PN-II-ID-PCE-3-0198.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of Automation, Electronics and MechatronicsUniversity of CraiovaCraiovaRomania

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