Multiple CLFs for Stabilization of Nonlinear Systems with Input Constraints

This paper considers stabilizing a nonlinear system with input constraints using switched control. The first result is that, for a given control Lyapunov function (CLF), a stabilizable set of initial conditions can be found. The paper then considers switching between multiple CLFs to increase the space of stabilizing inputs which also increases the set of stabilizable initial conditions. An algorithm is presented that identifies a subset of the known CLFs that may be used at the current time to produce stabilizing control inputs. While there are existing results for switched system stabilization using CLFs, stabilization for systems with input constraints is an original contribution. Sum of squares (SOS) methods are discussed for generating multiple CLFs, and examples are provided.