Overapproximating the reachable sets of LTI systems through a similarity transformation

We present a decomposition method for complexity reduction in reachability analysis and controller synthesis based on a series of transformations. The decomposition is guaranteed to yield weakly-coupled (lower dimensional) subsystems with disjoint control input across them. Reachable sets, computed independently for each subsystem, are back-projected and intersected to yield an overapproximation of the actual reachable set. Using an example we show that significant reduction in the computational costs can be achieved. This technique has considerable potential utility for use in conjunction with computationally intensive reachability tools.