Rate-limiter stability analysis comparing bifurcation and LMI-based approaches

The effect of rate-limiters in open loop unstable systems is studied. First order plants with a rate-limiter in the feedback loop are considered, leading to discontinuous second order differential systems. Two different analysis methods are applied. Firstly, through bifurcation analysis, the existence of a unstable limit cycle is proved and expressions for its size and period are provided. Next, a linear matrix inequalities based analysis is carried out and an ellipsoidal approximation of the basin of attraction is obtained. Finally, the advantages and disadvantages of each approach are highlighted.