In this note, we study a robust synchronization problem for multistable systems evolving on manifolds within an Input-to-State Stability (ISS) framework. Based on a recent generalization of the classical ISS theory to multistable systems, a robust synchronization protocol is designed with respect to a compact invariant set of the unperturbed system. The invariant set is assumed to admit a decomposition without cycles, that is, with neither homoclinic nor heteroclinic orbits. Numerical simulation examples illustrate our theoretical results.
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- Lyapunov methods
- Stability analysis
- Nonlinear systems
- Numerical stability
- robust control
- robust synchronization protocol
- multistable systems
- input-to-state stability framework
- ISS framework