On exponential bistability of equilibrium profiles of nonisothermal axial dispersion tubular reactors

    Research output: Contribution to journalArticlepeer-review


    Sufficient conditions are established for the exponential stability/instability of the equilibrium profiles for a linearized model of nonisothermal axial dispersion tubular reactors. The considered reactors are assumed to involve a chemical reaction of the form A → B, where A and B denote the reactant and the product, respectively, and where the Peclet numbers appearing in the energy and mass balance partial differential equations are assumed to be equal. First, different kinds of linearization of infinite-dimensional dynamical systems are presented. Then, the considered linearized model around any equilibrium is shown to be well-posed. Moreover, by using a Lyapunov-based approach, exponential stability is addressed. In the case when the reactor can exhibit only one equilibrium, it is shown that the latter is always exponentially stable. When three equilibrium profiles are exhibited, bistability is established, i.e. the stability pattern '(exponentially) stable - unstable - stable' is proven for the linearized model. The results are illustrated by some numerical simulations.

    Original languageEnglish
    Article number9159873
    Pages (from-to)3235-3242
    Number of pages8
    JournalIEEE Transactions on Automatic Control
    Issue number7
    Publication statusPublished - Jul 2021


    • Dispersion
    • Equilibrium profile
    • Gateaux-Frechet derivatives
    • Inductors
    • Lyapunov method
    • Mathematical model
    • Nonisothermal tubular reactor
    • Nonlinear infinite-dimensional system
    • Numerical models
    • Perturbation methods
    • Stability analysis
    • Two dimensional displays
    • Gâteaux-Fréchet derivatives


    Dive into the research topics of 'On exponential bistability of equilibrium profiles of nonisothermal axial dispersion tubular reactors'. Together they form a unique fingerprint.

    Cite this