Linear system

In systems theory, a linear system is a model for a sufficiently well-insulated part of nature, in which all occurring functions are linear maps.

A linear system are internal state variables, and a dynamic range that describes the temporal evolution of these state variables. Furthermore, there are observable quantities that are functions only of the internal state variables, however, and does not characterize the internal state clearly. From outside of the isolated area, there are interactions that may be accepted as a weak, but nevertheless modify the internal dynamics.

For example, can be a linear differential system ( ie a system with a continuous time, infinite and continuous range of values ​​system operators ) to the internal state of the external influences, and the externally observable signals represented as

Where, ,, time-dependent matrices of suitable dimension are, in particular, must be square. The matrices can be combined into a block matrix, which is then called system matrix.

A linear system is linear time-invariant system ( LTI system ), if the matrix system does not depend on time.

However, systems with discrete time and finite range of values ​​may be linear, if the corresponding linear images are defined on the amounts and operators. A typical example is a linear machine with the non-equivalence as a linear operation, such as a linear feedback shift register.