Abstract
Abstract The observability and detectability of a class of population balance models described by a partial integro-differential equation coupled with an ordinary differential equation is characterized for a simple two-species bioreactor model. By a direct calculation of the indistinguishable trajectories and employing the direct method of Lyapunov sufficient conditions for detectability are derived in terms of the cell division characteristic distributions. The cases of monotonic and non-monotonic growth rate functions are considered and the corresponding differences highlighted. An observer is designed with ensured convergence rate in the first moment of the distribution. Numerical simulation results illustrate the theoretical assessments.
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