Invariance control of normal forms with input driven internal dynamics

This paper addresses the problem of making a given state space region positively invariant while guaranteeing global exponential stability for a class of systems with reduced relative degree in normal form where the control variable appears in the internal dynamics. The linear subsystem is globally exponentially stabilized by a dissipativity approach. This allows the freedom to switch one control parameter at arbitrary times which is used to control a state space region positively invariant. A design method for the resulting invariance controller and the state space region is presented. The presented theory is evaluated by simulations of a peaking system.