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. 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 A {displaystyle A,}  ∈ L(X), B {displaystyle B,}  ∈ L(U, X), C {displaystyle C,}  ∈ L(X, Y) and D {displaystyle D,}  ∈ L(U, Y) the following equations determine a discrete-time linear time-invariant system: with x {displaystyle x,} (the state) a sequence with values in X, u {displaystyle u,} (the input or control) a sequence with values in U and y {displaystyle y,} (the output) a sequence with values in Y.