# State space analysis

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**State space analysis** is an advanced method for the investigation of dynamic systems. It relies on the analysis of state variables that are usually vectors comprising a critical system variable, its derivative and optionally additional variables.

The state variable description of a system has the form

*y* = **Hx** + *ju*

**x**: State of the system (column vector, *n* elements for an *n*th order system)

**F**: *n* * *n* system matrix

**G**: *n* * 1 input matrix (column matrix)

**H**: 1 * *n* output matrix (row matrix)

*j*: direct transmission term

*y*: system output

*u*: system input

## Example Edit

An ASIA element can be converted to state variable form with

.

The state variable form is then

## Reference Edit

- Franklin GF, Powell JD, Emami-Naeini A. Feedback Control of Dynamic Systems. Delhi: Pearson Education, 2002. ISBN 8178086751
- Dietrich, J. W. Signal Storage in Metabolic Pathways: The ASIA Element.
*kybernetiknet*, Vol. 1, No. 3. (2000), pp. 1-9.