Stabilizing feedback design for time delayed polynomial systems using kinetic realizations

M. ApS, 2017. The MOSEK Optimization Toolbox for MATLAB Manual. Version 8.1. https://docs.mosek.com/9.2/toolbox/index.html. Briat, 2017, Stability and performance analysis of linear positive systems with delays using input–output methods, Int. J. Control, 91, 1669, 10.1080/00207179.2017.1326628 Chellaboina, 2009, Modeling and analysis of mass-action kinetics, IEEE Control Syst., 29, 60, 10.1109/MCS.2009.932926 Chellaboina, 2004, Direct adaptive control of nonnegative and compartmental dynamical systems with time delay, 1235 G. Craciun, 2015. Toric Differential Inclusions and a Proof of the Global Attractor Conjecture. arXiv:1501.02860. Devane, 2016, Delay-independent asymptotic stability in monotone systems, IEEE Trans. Autom. Control, 61, 2625, 10.1109/TAC.2015.2498137 Feinberg, 1979, Lectures on Chemical Reaction Networks Franze, 2012, Constrained nonlinear polynomial time-delay systems: a sum-of-squares approach to estimate the domain of attraction, IEEE Trans. Autom. Control, 57, 2673, 10.1109/TAC.2012.2190189 Györi, 1988, Two approximation techniques for functional differential equations, Comput. Math. Appl., 16, 195, 10.1016/0898-1221(88)90180-0 Haddad, 2010 Haddad, 2004, Stability theory for nonnegative and compartmental dynamical systems with time delay, Syst. Control Lett., 51, 355, 10.1016/j.sysconle.2003.09.006 Hale, 1993 Hangos, 2001 Horn, 1972, Necessary and sufficient conditions for complex balancing in chemical kinetics, Arch. Ration. Mech. Anal., 49, 172, 10.1007/BF00255664 Horn, 1972, General mass action kinetics, Arch. Ration. Mech. Anal., 47, 81, 10.1007/BF00251225 Lipták, 2018, Approximation of delayed chemical reaction networks, React. Kinet. Mech. Catal., 123, 403, 10.1007/s11144-017-1341-5 Lipták, 2019, Stabilization of time delayed nonnegative polynomial systems through kinetic realization, 3138 Lipták, 2018, Semistability of complex balanced kinetic systems with arbitrary time delays, Syst. Control Lett., 114, 38, 10.1016/j.sysconle.2018.02.008 Lipták, 2016, Stabilizing kinetic feedback design using semidefinite programming, IFAC-PapersOnLine, 49, 12, 10.1016/j.ifacol.2016.10.744 Lipták, 2015, Computing zero deficiency realizations of kinetic systems, Syst. Control Lett., 81, 24, 10.1016/j.sysconle.2015.05.001 Lipták, 2016, Kinetic feedback design for polynomial systems, J. Process Control, 41, 56, 10.1016/j.jprocont.2016.03.002 Liu, 2009, Constrained control of positive systems with delays, IEEE Trans. Autom. Control, 54, 1596, 10.1109/TAC.2009.2017961 Lofberg, 2004, YALMIP : a toolbox for modeling and optimization in MATLAB, 284 Mahmoud, 2017, Recent progress in stability and stabilization of systems with time-delays, Math. Probl. Eng., 10.1007/978-3-319-55432-7 Márton, 2018, Distributed control of interconnected chemical reaction networks with delay, J. Process Control, 71, 52, 10.1016/j.jprocont.2018.09.004 MATLAB, 2014 Papachristodoulou, 2005, Robust stabilization of nonlinear time delay systems using convex optimization, 5788 Richard, 2003, Time-delay systems: an overview of some recent advances and open problems, Automatica, 39, 1667, 10.1016/S0005-1098(03)00167-5 Roussel, 1996, The use of delay differential equations in chemical kinetics, J. Phys. Chem., 100, 8323, 10.1021/jp9600672 van der Schaft, 2015, Complex and detailed balancing of chemical reaction networks revisited, J. Math. Chem., 53, 1445, 10.1007/s10910-015-0498-2 Smith, 1995, Monotone Dynamical Systems. An Introduction to the Theory of Competitive and Cooperative Systems, 41 Sontag, 2001, Structure and stability of certain chemical networks and applications to the kinetic proofreading model of T-cell receptor signal transduction, IEEE Trans. Autom. Control, 46, 1028, 10.1109/9.935056 Takeuchi, 1996 Vághy, 2019, Kinetic realization of delayed polynomial dynamical models, IFAC-PapersOnLine, 52, 45, 10.1016/j.ifacol.2019.07.008 Érdi, 1989