Distributed parameter system

Distributed parameter systems (as opposed to lumped parameter systems) refer to systems whose state-space is infinite-dimensional. A body whose state is heterogenous has a distributed parameter. It is usually described by partial differential equations.

An example of a distributed parameter system is a bar that extends from the origin to the point 1 and whose temperature (state) is given by the function T, where T(x) is the temperature at the point x, where x belongs to the interval from 0 to 1. Since T may have an infinite number of independent values, the state-space is infinite-dimensional.