Quantized-state systems: a DEVS Approach for continuous system simulation

A new class of dynamical systems, Quantized State Systems or QSS, is introduced in this paper. QSS are continuous time systems where the input trajectories are piecewise constant functions and the state variable trajectories—being themselves piecewise linear functions—are converted into piecewise constant functions via a quantization function equipped with hysteresis. It is shown that QSS can be exactly represented and simulated by a discrete event model, within the framework of the DEVS-approach. Further, it is shown that QSS can be used to approximate continuous systems, thus allowing their discrete-event simulation in opposition to the classical discrete-time simulation. It is also shown that in an approximating QSS, some stability properties of the original system are conserved and the solutions of the QSS go to the solutions of the original system when the quantization goes to zero.