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.

[1]  Martin Buss,et al.  Robust stabilization of SISO non-minimum phase nonlinear systems , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[2]  Martin Buss,et al.  Sufficient conditions for invariance control of a class of nonlinear systems , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[3]  M. Buss,et al.  Preliminary studies on geometric invariance control synthesis , 1999, 1999 European Control Conference (ECC).

[4]  Martin Buss,et al.  Rollover avoidance for steerable vehicles by invariance control , 2001, 2001 European Control Conference (ECC).

[5]  Martin Buss,et al.  Invariance control for a class of cascade nonlinear systems , 2002, IEEE Trans. Autom. Control..