Nonlinear Systems

Abstract

In the preceding sections only linear systems were studied. The real world is, however, generally nonlinear, and the use of linear models is always a source of approximations that are often justified by a number of considerations, such as:

• 1. The study of linear systems is far easier than that of nonlinear systems. General information on the behaviour of the system can be drawn in the first case, while the results obtained studying nonlinear systems are usually applicable only to a given set of conditions.

• 2. Many actual systems show a behaviour that can be modelled as being linear, at least in a broad range of conditions.

• 3. Even if a system is essentially nonlinear, it is possible, with a few exceptions, to linearize its behaviour for very small variations of its state in the vicinity of given conditions. In such case the advantages in 1 can be exploited and a general solution for the behaviour in the small can be obtained.