Distributed parameter system (as opposed to a lumped parameter system) refers to system whose state-space is infinite-dimensional. A body whose state is heterogenous has a distributed parameter. It is usually described by partial differential equations. A system is an assemblage of inter-related elements comprising a unified whole. ... A heterogeneous compound, mixture, or other such object is one that consists of many different items, which are often not easily sorted or separated, though they are clearly distinct. ... In mathematics, and in particular analysis, a partial differential equation (PDE) is an equation involving partial derivatives of an unknown function. ...
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 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].
(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.) In mathematics, the dimension of a vector space V is the cardinality (i. ...
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