Sampling Intervals Enlargement for a Class of Parabolic Sampled-Data Observers

Tarek Ahmed-Ali (1) , E Fridman (2) , Fouad Giri (1) , Françoise Lamnabhi-Lagarrigue (3)

1 Equipe Automatique - Laboratoire GREYC - UMR6072
2 Department of Electrical Engineering
3 L2S - Laboratoire des signaux et systèmes

The problem of state observation is addressed for a class of parabolic systems governed by linear diffusion PDEs. An observer is designed that provides online estimates of the system (spatially distributed) state, based on time sampled output measurements. The observer is a fixed-gain involving an inter-sample output predictor, making the state trajectories (at the different spatial positions) continuous in time. The observer convergence is analyzed using Lyapunov's direct method, Writtinger's inequalities and other tools. Sufficient conditions for exponential convergence are established in terms of LMIs involving the sampling period and the observer gain. Interestingly, the conditions entail no limitation on the spatial domain length and no persistent excitation requirement.

Domaines: Automatique; Automatique / Robotique

Tarek Ahmed-Ali, E Fridman, Fouad Giri, Françoise Lamnabhi-Lagarrigue. Sampling Intervals Enlargement for a Class of Parabolic Sampled-Data Observers. 2015 SIAM Conference on Control and its Applications, Jul 2015, Paris, France. ⟨hal-01260392⟩