Sequences of Discrete Abstractions for Piecewise Affine Systems*

Symbolic models have been recently used as a sound mathematical formalism for the formal verification and control design of purely continuous and hybrid systems. In this paper we propose a sequence of symbolic models that approximates a discrete–time Piecewise Affine (PWA) system in the sense of approximate simulation and converges to the PWA system in the so–called simulation metric. Symbolic control design is then addressed with specifications expressed in terms of non–deterministic finite automata. A sequence of symbolic control strategies is derived which converges, in the sense of simulation metric, to the maximal controller solving the given specification on the PWA system.