On stability of invariance controlled linear systems

Invariance control addresses the problem of control of nonlinear systems in the presence of state constraints. Admissibility with the constraints is guaranteed by keeping an admissible subset of state space positively invariant by switching of the control on the boundary of the set. This paper discusses application of invariance control on the special case of linear systems. For low order systems controlled by linear state feedback, it is shown that the resulting switching invariance control loop is asymptotically stable. The effectiveness of the approach is demonstrated by simulations of an example system.