Block-wise discretization accounting for structural constraints

This paper presents an approximate discretization method, named Mixed Euler-ZOH (mE-ZOH), which can be applied to any continuous-time linear system. This method has been explicitly developed to preserve the system sparsity, a property that is particularly important when dealing with the analysis and design of distributed controllers for large-scale systems. In terms of stability preservation as a function of the sampling interval, we show that mE-ZOH outperforms the classical forward Euler (fE) approach, which is the only known discretization method guaranteeing the preservation of sparsity for all possible sampling times. It is then shown that this new discretization method is capable of preserving stability for all sampling times for a wide classes of dynamical systems, including the important class of positive systems. Besides stability, also positivity of the resulting discrete-time system is preserved, contrarily to what happens for the fE approach. A couple of examples are reported to illustrate the main theoretical results of the paper.