Lyapunov Function Partial Differential Equations for Stability Analysis of a Class of Chemical Reaction Networks. Issue 2 (2020)

• Record Type: Journal Article
• Authors: Wu, Shan; Lu, Yafei; Gao, Chuanhou
• Is Part Of: IFAC-PapersOnLine. Volume 53:Issue 2(2020)
• Page Start: 11509
• Page End: 11514
• Publication Date: 2020
• Subjects: CBP-CRNs -- Lyapunov function PDEs -- the generalized pseudo-Helmholtz free energy function; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2020.12.602
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: We investigate a broad family of chemical reaction networks (CRNs) assigned with mass action kinetics, called complex-balanced-produced-CRNs (CBP-CRNs), which are generated by any given complex balanced mass action system (MAS) and whose structures depend on the selection of producing matrices. Unluckily, the generally applied pseudo-Helmholtz free energy function may fail to act as a Lyapunov function for the CBP-CRNs. Inspired by the method of Lyapunov function partial differential equations (PDEs), we construct one solution of their corresponding Lyapunov function PDEs, termed as the generalized pseudo-Helmholtz free energy function, and we further show that solution can behave as a Lyapunov function to render the asymptotic stability for the CBP-CRNs. This work can be taken as an argument of the conjecture that Lyapunov function PDEs approach can serve for any MAS.