A second-order approximation for DEVS simulation of continuous systems

In this article, based on the methodology of discrete event simulation of continuous systems via quantized state systems (QSS), a new second-order approximation, called second-order quantized state systems (QSS2), is proposed. This new approximation, which satisfies the same stability and convergence properties that were deduced for QSS in previous works, also allows reducing the number of calculations with respect to the former method. It is shown that in the particular case of linear time-invariant (LTI) systems, the QSS2 can be exactly represented by a DEVS model, and in nonlinear systems, an approximated DEVS model can be also obtained. For the LTI case, a closed formula giving the necessary quantization that allows achieving a bound in the error during the whole simulation is deduced. This formula, which stands for both QSS and QSS2 approaches, also proves that for any quantization, the error is always bounded.