Observer Design For Multidimensional Parabolic Systems⁎. Issue 2 (2019) - Montoya, Cristhian; Moreno, Jaime A.; Teresa, Luz de
Abstract: In this paper we present some observer designs for infinite dimensional parabolic systems, defined in multidimensional space domains. We consider two observation scenarios. (i) When the state is measured in an open (possibly small) subdomain of the space domain we obtain an exponentially convergent observer with gain for a semilinear parabolic system in arbitrary domains. (ii) When the state is measured along a line orthogonal to the sides of a rectangle in ℝ 2 we derive an observer for a linear parabolic system. The mathematical setting relies upon the semigroup theory for n-dimensional autonomous systems as well as on Fourier analysis.