A thermodynamic Lyapunov Approach to the Stability Analysis of a Nonlinear Irreversible Process Having Multiplicity


Thuan C. Nguyen(1), Ha N. Hoang(2*)

(1) University of Technology, VNU-HCM, 268 Ly Thuong Kiet Str., Dist. 10, HCM City, Vietnam
(2) University of Technology, VNU-HCM, 268 Ly Thuong Kiet Str., Dist. 10, HCM City, Vietnam; Duy Tân University, 254 Nguyen Van Linh Road, Da Nang, Vietnam
(*) Corresponding Author


Following the second law of thermodynamics, the entropy is always created in irreversible processes such as reacting systems, etc. Under certain operating conditions, the reaction system can be operated with multiple steady states (also called the steady state multiplicity behavior). This behavior is considered for the illustration of the stability analysis of all possible steady states by Lyapunov methods using thermodynamics. More precisely, a novel symmetric storage function (or Lyapunov function candidate) is proposed on the basis of the so-called (non-symmetric) thermodynamic availability function. The acid-catalyzed hydration of 2-3-epoxy-1-propanol to glycerol subject to steady state multiplicity is used for further technical developments. The results are discussed with the inclusions of the simulations.


Dynamical systems, multiplicity, Lyapunov function, stability, control, thermodynamics

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DOI: https://doi.org/10.22146/ajche.49561

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