Stability of limit cycles in feedback systems containing a relay

The stability of limit cycles in feedback systems containing a relay is investigated in the paper. A necessary and sufficient condition for limit-cycle stability as well as a second necessary condition are derived. The conditions are used in conjunction with the exact limit-cycle solution which is readily found for relay systems. An approximate version of these two conditions, using the describing-function solution for the limit cycles, is also proposed. Extensive simulation results are given to substantiate the theory developed.