Hierarchical hysteresis switching

We describe a new switching logic, called “hierarchical hysteresis switching”, and establish a bound on the number of switchings produced by this logic on a given interval. The motivating application is the problem of controlling a linear system with large modeling uncertainty. We consider a control algorithm consisting of a finite family of linear controllers supervised by the hierarchical hysteresis switching logic. In this context, the bound on the number of switchings enables us to prove stability of the closed-loop system in the presence of noise, disturbances, and unmodeled dynamics