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Finite-state models of control systems were proposed by several researchersas a convenient mechanism to synthesize controllers enforcing complexspecifications. Most techniques for the construction of such symbolic modelshave two main drawbacks: either they can only be applied to restrictive classesof systems, or they require the exact computation of reachable sets. In thispaper, we propose a new abstraction technique that is applicable to any smoothcontrol system as long as we are only interested in its behavior in a compactset. Moreover, the exact computation of reachable sets is not required. Theeffectiveness of the proposed results is illustrated by synthesizing acontroller to steer a vehicle.

Symbolic models for nonlinear control systems without stability assumptions