Distributed parameter system

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

With U, X and Y Hilbert spaces and ${\displaystyle A\,}$ ∈ L(X), ${\displaystyle B\,}$ ∈ L(U, X), ${\displaystyle C\,}$ ∈ L(X, Y) and ${\displaystyle D\,}$ ∈ L(U, Y) the following equations determine a discrete-time linear time-invariant system:

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