I have done some research on the control and modeling of biological systems and chemostats. Here is a list of papers where you can find results on biological systems and chemostats.

• I. Karafyllis and M. Krstic, “An ODE Observer for Lyapunov-Based Global Stabilization of a Bioreactor Nonlinear PDE”, Feedback Stabilization of Controlled Dynamical Systems, Nicolas Petit (Ed.), Lecture Notes in Control and Information Sciences, Vol. 473, Springer, 2017.

• I. Karafyllis, C. Kravaris, L. Syrou and G. Lyberatos, “A Vector Lyapunov Function Characterization of Input-to-State Stability with Application to Robust Global Stabilization of the Chemostat”, European Journal of Control, 14(1), 2008, pp. 47-61.

• I. Karafyllis, C. Kravaris and N. Kalogerakis, “Relaxed Lyapunov Criteria for Robust Global Stabilization of Nonlinear Systems”, International Journal of Control, 82(11), 2009, pp. 2077-2094.

• I. Karafyllis and Z.-P. Jiang, “A New Small-Gain Theorem with an Application to the Stabilization of the Chemostat”, International Journal of Robust and Nonlinear Control, 22(14), 2012, pp. 1602–1630.

• I. Karafyllis and Z.-P. Jiang, “Reduced Order Dead-Beat Observers for the Chemostat”, Nonlinear Analysis Real World Applications, 14(1), 2013, pp. 340–351.

• I. Karafyllis and M. Krstic, “Stability of Integral Delay Equations and Stabilization of Age-Structured Models”, ESAIM Control, Optimisation and Calculus of Variations, 23(4), 2017, pp. 1667-1714.

• K. Schmidt, I. Karafyllis and M. Krstic, “Yield Trajectory Tracking for Hyperbolic Age-Structured Population Systems”, Automatica, 90, 2018, pp. 138-146.

• P.-E. Haacker, I. Karafyllis, M. Krstic and M. Diagne, “Stabilization of Age-Structured Chemostat Hyperbolic PDE with Actuator Dynamics”, International Journal of Robust and Nonlinear Control, 34(10), 2024, pp. 6741-6763.

• C. Veil, M. Krstic, I. Karafyllis, M. Diagne and O. Sawodny, “Stabilization of Predator-Prey Age-Structured Hyperbolic PDE when Harvesting both Species is Inevitable”, to appear in IEEE Transactions on Automatic Control (see also arXiv:2410.06823 [eess.SY]).

• I. Karafyllis, E. Loko, M. Krstic and A. Chaillet, “Global Stabilization of Chemostats with Nonzero Mortality and Substrate Dynamics”, submitted to IEEE Transactions on Automatic Control (see also arXiv:2502.09310 [math.OC]).