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Chapitre D'ouvrage Année : 2023

Saturated Boundary Stabilization of Partial Differential Equations Using Control-Lyapunov Functions

Résumé

This chapter reviews some recent results on the boundary stabilization of different classes of partial differential equations. In order to provide a self-content chapter with consistent control objectives and notation, we first review the finite-dimensional case. Controllability and observability conditions for linear ordinary differential equations are recalled together with some basic Lyapunov theory for the stability analysis and the design of saturated controllers. Then we address the boundary control problem for the stabilization of a reaction-diffusion equation by means of numerically tractable design methods while considering different norms and possible constraints on the amplitude of the inputs. Finally similar control design problems will be studied for the stabilization of the Korteweg–de-Vries equation and the wave equation.
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Dates et versions

hal-04070717 , version 1 (16-04-2023)

Identifiants

Citer

Hugo Lhachemi, Christophe Prieur. Saturated Boundary Stabilization of Partial Differential Equations Using Control-Lyapunov Functions. Jean-Michel Coron, Tatsien Li and Zhiqiang Wang. Control of Partial Differential Equations, 24, WSPC/HEP, pp.81-164, 2023, Series in Contemporary Applied Mathematics, ⟨10.1142/9789811271632_0002⟩. ⟨hal-04070717⟩
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