Distributed parameter systems

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

An example of a distributed parameter system is a bar on the real line 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 and x belongs to the interval $[0,1]$ . The (infinite-dimensional) state-space could be, e.g., the space of continuous functions on $[0,1]$ , if the temperature is assumed to vary continuously along the bar.

(That space is infinite-dimensional because T may simultaneously have an infinite number of independent values (at different values of x). For an exact explanation, see Hamel dimension.)