Feedback control of switched nonlinear systems using multiple Lyapunov functions

This work proposes a hybrid nonlinear control methodology for a broad class of switched nonlinear systems with input constraints. These systems combine both continuous dynamics and discrete events that govern the changes in the continuous dynamics. The key feature of the proposed methodology is the integrated synthesis, via multiple Lyapunov functions, of "lower-level" bounded nonlinear controllers and "upper-level" switching laws that orchestrate the transitions between the constituent dynamical modes of the switched system and their respective controllers. The bounded controllers enforce stability within the individual dynamical modes while the switching scheme ensures stability of the overall system despite the combined continuous/discrete dynamics and the input constraints. The proposed control methodology is successfully applied to an exothermic chemical reactor with continuous dynamics, discrete events and input constraints.