Hyper-Rectangular Over-Approximations of Reachable Sets for Linear Uncertain Systems

In this paper, we propose a novel method, using the frameworks of differential inequalities and essentially nonnegative matrices, to construct hyper-rectangular over-approximations of reachable sets for a general class of linear uncertain systems whose nominal parameters and bounds on uncertainties are time-varying. The motivation of this paper is the need for relatively accurate yet computationally inexpensive over-approximation method that is practical in various control methods especially abstraction-based control synthesis. We demonstrate the proposed method in an illustrative example and two control examples related to abstraction-based control synthesis. In these examples, the proposed method shows excellent results in terms of representing reachable sets with reasonable accuracy and allowing the implementation of time-varying control input signals.