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

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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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