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)

1 GIPSA-SYSCO - GIPSA - Systèmes non linéaires et complexité
2 GIPSA-SLR - GIPSA - Systèmes linéaires et robustesse

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.

Domaines: Automatique / Robotique; Automatique; Optimisation et contrôle [math.OC]; Systèmes et contrôle [cs.SY]

Federico Bribiesca Argomedo, Emmanuel Witrant, Christophe Prieur. D1-Input-to-State Stability of a Time-Varying Nonhomogeneous Diffusive Equation Subject to Boundary Disturbances. ACC 2012 - American Control Conference, Jun 2012, Montréal, Canada. pp.2978-2983, ⟨10.1109/ACC.2012.6315060⟩. ⟨hal-00676534⟩