Reachability Analysis of Continuous-Time Piecewise Linear Systems

This paper presents a new approach to the reachability problem for a class of hybrid systems called Piecewise Linear Systems (PLS). The principal tool used is the impact map between switching surfaces. The method consists of specifying a ellipsoidal set on the initial switching surface and finding upper- and lower-bound estimates of the possible reach sets using tools such as the S-procedure to set up linear matrix inequalities, of which numerical solutions are then computed.