Schur-based decomposition for reachability analysis of linear time-invariant systems

We present a method for complexity reduction in reachability analysis and controller synthesis via a Schur-based decomposition for LTI systems. The decomposition yields either decoupled or weakly-coupled subsystems, each of lower dimension than the original system. Reachable sets, computed for each subsystem, are back-projected and intersected to yield an overapproximation of the actual reachable set. Evaluating our method for a variety of examples (3D, 4D, and 8D), 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.