Guaranteed Simulation of Dynamical Systems with Integral Constraints and Application on Delayed Dynamical Systems

A reachable set computation method for dynamical systems with an integral constraint over the input set is proposed. These models are typical in robustness analysis when studying the impact of bounded energy noises over a system response and can also model a large family of complex systems. The reachable set is over-approximated using a guaranteed set-based integration method within the interval arithmetic framework.