Abstract
Optimal control and reachability analysis of continuous-state systems often require computational algorithms with high complexity. The use of discrete-state abstractions of continous-state systems reduces such problems to path-planning problems on directed graphs with a finite number of nodes, which can be computed efficiently. In this paper, we propose a method to design discrete abstractions of stabilizable discrete-time linear systems based on the notion of approximate bisimulation. Moreover, we show that a suboptimal solution to optimal control problems with a known bound on performance deterioration is obtained by making use of discrete abstraction.
