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Symbolic models have been recently used as a sound mathematical formalism forthe formal verification and control design of purely continuous and hybridsystems. In this paper we propose a sequence of symbolic models thatapproximates a discrete-time Piecewise Affine (PWA) system in the sense ofapproximate simulation and converges to the PWA system in the so-calledsimulation metric. Symbolic control design is then addressed withspecifications expressed in terms of non-deterministic finite automata. Asequence of symbolic control strategies is derived which converges, in thesense of simulation metric, to the maximal controller solving the givenspecification on the PWA system.

Symbolic Models and Control of Discrete-Time Piecewise Affine Systems: An Approximate Simulation Approach