Direct Verification of Linear Systems with over 10000 Dimensions

We evaluate a recently-proposed reachability method on a set of high-dimensional linear system benchmarks taken from model order reduction and presented in ARCH 2016. The approach uses a state-set representation called a generalized star set and the principle of superposition of linear systems to achieve scalability. The method was previously shown to have promise in terms of scalability for direct analysis of large linear systems. For each benchmark, we also compare computing the basis matrix, a core part of the reachability method, using numerical simulations versus a matrix exponential formulation. The approach successfully analyzes systems with hundreds of dimensions in minutes, and can scale to systems that have over 10000 dimensions with a computation time ranging from tens of minutes to tens of hours, depending on the desired time step.