Estimating reachable sets for two-dimensional linear discrete systems (Q1089290)

We are concerned with the problem of estimating the reachable set \({\mathcal R}\) for a two-dimensional linear discrete-time system with bounded controls. Different approaches are adopted depending on whether the system matrix has real or complex eigenvalues. For the complex eigenvalue case, the quasi-periodic nature of minimum time trajectories is exploited in developing a simple, but often accurate, procedure. For the real eigenvalue case, overestimates of reachable sets can be trivially obtained using a decomposition method.