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In this paper, we consider an observer design problem of a time fractional reaction–diffusion system with space-dependent coefficients and measurement of weighted spatial averages. Different from the boundary measurement, here, the output is a weighted spatial average of the state over the entire spatial domain. In order to apply the backstepping approach to obtain the observer gains, we first use a conversion of weighting functions to transform the error system into an intermediate system. With a change of variable, this intermediate system is then converted into the final target system with boundary measurement where backstepping is easily applicable. The resultant observer realises Mittag-Leffler convergence of the error system. Finally, numerical simulations are provided to check the effectiveness of the proposed observer.

Observer design for time fractional reaction–diffusion systems with spatially varying coefficients and weighted spatial averages measurement