On incrementally bounded systems

A system defined on a domain D ⊆ ℝⁿ is said to be incrementally bounded by K ≥ 0 if for every point x₀ ∈ D and any ε > 0, the distance between trajectories starting at x₀ and any x´₀ in some neighborhood of x₀ never exceeds K+ε for all t ≥ 0. Bisimulation functions for continuous systems provide sufficient conditions for a system to be incrementally bounded. Conditions are presented for a second class of functions that can determine a lower bound on the incremental bound K. As an example, sum-of-squares (SoS) is used to find such a bound for a particular polynomial system. The concluding section discusses possible applications of these results.