Hybrid systems present distinct challenges for numerical methods that attempt to accurately approximate behaviors of these systems. Near the mode transition boundaries, a simulation often has to reduce time steps in order to produce accurate behaviors. This paper considers an interesting class of behaviors at the boundaries, the sliding motion. Sliding mode systems move along sliding surfaces because of continuous interaction between two alternating operating modes. However, unmodeled small, higher order, dynamic effects or discrete-time numerical simulation could introduce chattering along the surface. To reduce simulation error, the step size in a numerical integration is kept small to capture the fast chattering motion. As a result, simulated time progresses only in small increments, and the slower, sliding movement along the switching surface is not simulated efficiently.
Based on a physical model semantics, we have developed a sliding mode simulation algorithm using the Filippov equivalence of dynamics. Our implementation has shown that the simulation introduces a very small error while maintaining consistency of the temporal behavior of the slow component along the sliding surface. The algorithm performs well in several engineering applications where discontinuities in physical behavior cause the system to undergo mode switches.