  This article considers a model formulation and an adaptive observer design
for the simultaneous estimation of the state of charge and crossover flux in
disproportionation redox flow batteries. This novel nonaqueous battery
chemistry allows a simple isothermal lumped parameter model to be formulated.
The transport of vanadium through the porous separator is a key unknown
function of battery variables and it is approximated in the space of continuous
functions. The state and parameter observer adaptation laws are derived using
Lyapunov analysis applied to the estimation error, the stability and
convergence of which are proved. Numerical values of observer gains are
calculated by solving a polytopic linear matrix inequality and equality problem
via convex optimization. The performance of this design is evaluated on a
laboratory flow battery prototype, and it is shown that the crossover flux can
be considered a linear function of state of charge for this battery
configuration during self-discharge.
