Observability Gramian

Observability Gramian: The Observability Gramian is a Gramian used in optimal control theory to determine whether or not a linear system is observable.

For a linear system described by

$\dot{x} = A x + B u$

$y = C x + D u \,$

The observability Gramian is given by

$W_o (t) = \int\limits_0^t e^{A^T \tau} C^T C e^{A \tau} d\tau$

If and only if the matrix $W o$ is nonsingular for every $t > 0$ , the pair $(A, C)$ is observable.

See also

Controllability Gramian

Gramian matrix

References

Categories:
Control theory
Mathematics stubs

Игры ⚽ Нужно решить контрольную?

Gramian matrix — In linear algebra, the Gramian matrix (or Gram matrix or Gramian) of a set of vectors v 1,dots, v n in an inner product space is the symmetric matrix of inner products, whose entries are given by G {ij}=(v i|v j).An important application is to… … Wikipedia
Controllability Gramian — In control theory, the controllability Gramian is a Gramian used to determine whether or not a linear system is controllable. For the time invariant linear system the controllability Gramian is given by If the matrix Wc is nonsingular, i.e. Wc… … Wikipedia
Hankel singular value — In control theory, Hankel singular values, named after Hermann Hankel, provide a measure of energy for each state in a system. They are the basis for balanced model reduction, in which high energy states are retained while low energy states are… … Wikipedia
List of mathematics articles (O) — NOTOC O O minimal theory O Nan group O(n) Obelus Oberwolfach Prize Object of the mind Object theory Oblate spheroid Oblate spheroidal coordinates Oblique projection Oblique reflection Observability Observability Gramian Observable subgroup… … Wikipedia

Academic Dictionaries and Encyclopedias