On Reachability Problem for Linear Hybrid Systems

In this paper we present new decidability results, wider decidable classes of linear hybrid systems with linear vector field of the form x=Ax+Bu at each discrete location. Combination of the systematic treatment for the decidability problems of the linear differential systems x=Ax+Bu by H. Anai et al [4] and the framework dealing with decidability problems of hybrid systems based on the mathematical logic and model theory introduced by G. Lafferriere et al [13, 14] enables these decidability results. Moreover, we also discuss some extensions of these decidability results.