A Stabilization Approach of a CSTR with Two Arbitrarily Switching Modes Using a Common Control Lyapunov Function

Abdessamad Abdelhedi(1*), Lassaâd Sbita(2)

(1) National Engineering School of Gabes, Research Unit of Photovoltaic, Wind and Geothermal Systems, University of Gabes, Gabes, Tunisia
(2) National Engineering School of Gabes, Research Unit of Photovoltaic, Wind and Geothermal Systems, University of Gabes, Gabes, Tunisia
(*) Corresponding author

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This paper presents a study of stabilization for a class of the nonlinear switched systems. This study, indeed, is based on stabilization by using control Lyapunov functions. Firstly, a necessary and sufficient condition of stabilization is clarified. This condition hinges on the existence of a common control Lyapunov functions in the switching subsystems. The common controlled Lyapunov function is explicitly built by using controlled Lyapunov functions associated with the sub-systems. Secondly, a stabilization controller is designed for the nonlinear switching system by using the common Lyapunov function theory. Lastly, to illustrate this study, the example of a continuous stirred tank reactor (CSTR) with two modes is deemed to show the applicability of the suggested approach.
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Switched Systems; Stabilization; Control Lyapunov Functions; CSTR

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