Robust output synchronization of phase planar systems

We propose a technique to synchronize, under the master/slave synchronization scheme, two planar systems represented by phase state variables; we name them phase planar systems. The coupling signal has a discontinuous term that produces a closed-loop system having good characteristics of robustness with respect to bounded disturbances and parametric variations, and guarantees exponential convergence to the synchronization state. In general, the coupling signal needs the full state vector of both systems, but because we assume that only the system outputs are available, we include a robust observer. This observer also guarantees exponential convergence to the state of the plant in spite of the existence of bounded disturbances and parametric variations; this characteristic facilitates the stability analysis of the closed-loop system. The performance of the synchronization technique is illustrated with experimental results.