Quadratic stability of process systems in generalized lotka-volterra form

Abstract

The global and local stability of process systems in generalized Lotka-Volterra form is studied in this paper using entropy-like and quadratic Lyapunov function candidates. The global stability check for LV models is performed by solving an LMI for a diagonal positive semi-definite matrix using singular perturbation technique. It is shown that a quadratic Lyapunov function can also be determined by solving linear matrix inequalities (LMIs). In addition, the quadratic stability neighborhood is convex in the space of the quasi-monomials and can be estimated by computing its corner points using LMIs. Furthermore, it is proved that quadratic stability with a diagonal weighting matrix enables to construct a dissipative-Hamiltonian description of the system. The developed methods are illustrated on the model of a continuously stirred tank reactor with a nonlinear reaction system.