Symbolic models for linear control systems with disturbances

A recent trend in the control systems community is the study of appropriate symbolic abstractions capturing the behavior of continuous and hybrid systems. This approach provides a common mathematical language to describe physical systems as well as software and hardware, and is therefore particularly appealing when dealing with the design of embedded systems. In this paper we address the construction of symbolic models for the class of linear control systems with politopically bounded states and disturbances. We show that under an asymptotic stabilizability assumption, it is always possible to construct a symbolic model that approximates the control system with a precision that is chosen a priori, as a design parameter. While in previous approaches in the existing literature, the construction of symbolic models relied on a (arbitrary) choice of a finite number of control signals, the symbolic model that we propose, captures any (control and disturbance) input. Therefore, the proposed model provides a finer description of the continuous model than the existing ones and this feature translates into a more efficient controller synthesis process. Furthermore, the computation of the symbolic model can be performed by resorting to linear matrix inequalities.