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Significant improvements and a thorough complementary analysis are proposed for an infinite-dimensional sliding mode state observer for a linear reaction–convection–diffusion system subject to bounded disturbances, that was analyzed in Dimassi et al. (2018). Compared to the previous article, the observer model features a simplified discontinuous input applied on the error dynamics such that the on-line computation of the state time derivative at the boundary is no longer needed. An abstract representation of the state observer is given, and a particular attention is paid to its well-posedness on a Sobolev space despite the discontinuity. The exponential stability of the error dynamics is established by considering one boundary measurement and a continuous approximation of the discontinuous input. The results are illustrated by means of numerical simulations.
- Distributed parameter systems
- Sliding mode
- Sobolev space
- State observer
- Strongly continuous semigroup