This paper discusses the designing of switched linear system to the modeling of the air path of diesel engines for purpose of fault detection. The main goal for further investigation is to extend our proposed H-infinity robust filtering procedure for the entire engine operational range. For this reason, an appropriate modelling approach are needed to handle the nonlinear engine model. Our idea is to design a switched system being reasonable for approximation of the main attribute of the nonlinear system, moreover, it can be handled as a linear system. This is done by creating linear time-invariant systems for various operating points of a nonlinear plant and, based on a pre-defined switching rule, we switch between them. After a short introduction of mathematical results how to derive a switched system, we explain the steps of the designed procedure. Finally, the applicability is demonstrated based on the model of air path of diesel engines via MATLAB simulations.

The paper serves as a review on the basic results showing how functional analytic tools have been applied in numerical analysis. It deals with abstract Cauchy problems and present how their solutions are approximated by using space and time discretisations. To this end we introduce and apply the basic notions of operator semigroup theory. The convergence is analysed through the famous theorems of Trotter and Kato, Lax, and Chernoff. We also list some of their most important applications.