Sufficient conditions for invariance control of a class of nonlinear systems

This paper addresses control of nonlinear, control input affine systems coupled with a controllable linear subsystem via state and control variables. The proposed method of Invariance Control achieves positive invariance of a state space region and exponential stability of the linear subsystem. A design method for a switching controller and sufficient conditions for positive invariance are presented. The proposed theory is illustrated by simulations of a non-minimum phase system with partly stable zero-dynamics.