D1-Input-to-State Stability of a Time-Varying Nonhomogeneous Diffusive Equation Subject to Boundary Disturbances

Federico Bribiesca Argomedo 1, * Emmanuel Witrant 2 Christophe Prieur 1
* Corresponding author
1 GIPSA-SYSCO - SYSCO
GIPSA-DA - Département Automatique
2 GIPSA-SLR - SLR
GIPSA-DA - Département Automatique
Abstract : D1-Input-to-state stability (D1ISS) of a diffusive equation with Dirichlet boundary conditions is shown, in the L2-norm, with respect to boundary disturbances. In particular, the spatially distributed diffusion coefficients are allowed to be time-varying within a given set, without imposing any constraints on their rate of variation. Based on a strict Lyapunov function for the system with homogeneous boundary conditions, D1ISS inequalities are derived for the disturbed equation. A heuristic method used to numerically compute weighting functions is discussed. Numerical simulations are presented and discussed to illustrate the implementation of the theoretical results.
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Federico Bribiesca Argomedo, Emmanuel Witrant, Christophe Prieur. D1-Input-to-State Stability of a Time-Varying Nonhomogeneous Diffusive Equation Subject to Boundary Disturbances. American Control Conference (ACC 2012), Jun 2012, Montréal, Canada. pp.2978-2983, ⟨10.1109/ACC.2012.6315060⟩. ⟨hal-00676534⟩

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