Design of a controller of switched nonlinear systems based on multiple Lyapunov functions

Abstract

In thiswork,we focus on the stabilization issue of a class of non-minimum phase switched nonlinear systems where the internal dynamics of each mode may be unstable and uncontrollable.We develop a hybrid nonlinear control technique based on the coupling between bounded nonlinear feedback controllers and the switching laws designed to stabilize the transitions between the stability regions associated to each modes arising from the limitations imposed by the input constraints. The key feature of the proposed approach is based on the formalism of the input–output feedback linearization. The performed developments largely rely on Hauser’s approximation and multiple Lyapunov functions. In summary, the synthesized controllers can guarantee the stability of individual modes while switching law that will be generating ensures overall system stability. The differences between the switching strategies, and their implications on the switching logic, are discussed. A non-minimum phase Continuously Stirred Tank Reactor (CSTR) illustrates the efficiency of the proposed approach.