Distributed parameter system

A distributed parameter system (as opposed to a lumped parameter system) is a system whose state space is infinite-dimensional. Typical examples are systems described by partial differential equations or by delay 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.)

See also

• Control theory
• State space

External links

• McCann Science: "Distributed Parameter Systems, models, control..."
• Laboratoire d’É Thermiques (France). Modeling Distributed Parameters Systems..."

t