Semi-global analysis of relay feedback systems

This paper presents semi-global sufficient stability conditions of limit cycles for relay feedback systems. Local stability conditions exist. These are based on analyzing the linear part of the Poincare map. We know that when a certain limit cycle satisfies those local conditions, a neighborhood around the limit cycle exists such that any trajectory starting in this neighborhood converges to the limit cycle as time goes to infinity. However, tools to characterize this neighborhood do not exist. In this work, we present conditions, in the form of linear matrix inequalities (LMI), that guarantee the stability of a limit cycle in a reasonably large set around it. These results differ from previous local results as they take into account the high order terms of the Poincare map.