Stability of a class of nonlinear stirred tank reactor

We consider a continuous stirred tank reactor containing n chemical or biological species X_i; we suppose that this reactor is isothermal (it can be also the zero dynamics of a thermal reactor if we are able to control the heat transfer and measure the temperature T in the reactor); the basic reactions are of the form X_i → X_j and the kinetics law of this reaction depends only of X_i, but is nonlinear; we give some sufficient conditions giving the global asymptotic stability of the equilibrium. The kinetics laws can depend on the temperature, on the time, and be partially unknown; they are not necessarily increasing with respect to X_i, but are rather subject to “positivity” with respect to the equilibrium.