LIMIT CYCLE BIFURCATION INDUCED BY RATE-LIMITERS IN THE FEEDBACK LOOP

The effect of rate-limiters in open-loop unstable linear systems is studied. The case of first order plants is considered, which after including the rate-limiter gives rise to a discontinuous second order dynamical system. The existence of one unstable limit cycle, born through a bifurcation at infinity and bounding the attraction basin of the origin, is shown. Analytical expressions for the amplitude and period of the bifurcating limit cycle are provided. It is also conjectured that n-dimensional open-loop unstable linear systems with a rate-limiter in the loop cannot be globally asymptotically stable.