Reachability Analysis of Linear Systems with Stepwise Constant Inputs

Reachability analysis is one major approach for safety verification of continuous and hybrid dynamical systems. In this paper we present a new approach to calculate the reachable states of linear systems with uncertain inputs under the assumption that the inputs are stepwise constant. The original system S with inputs is transformed into a system S′ without inputs such that the reachability problem of S can be reformulated as a problem that involves only S′ and thus the inputs need no longer to be considered. Finally, we show that this approach is in accordance with existing ones.