# system model

Let $t=1,2,\ldots$ denote discrete time instants. By a system model we mean a mathematical model defined by a conditional probability density function $f(y_{t}|u_{t},d(t-1))$ where

$y_{t}$

is the system output in time $t$,

$u_{t}$

is the system input and

$d(t-1)$

denotes the sequence of data $d_{0},\ldots,d_{t-1}$ where $d_{t}=(u_{t},y_{t})$.

Such a system has time-invariant (constant) parameters. If the model parameters are unknown (uncertain, variable), we introduce the definition in the form $f(y_{t}|u_{t},d(t-1),\theta)$. Here, $\theta$ is a (possibly multi-dimensional) parameter.

## References

• 1 Peterka, V., Bayesian Approach to System Identification, in Trends and Progress in System Identification, P. Ekhoff, Ed., pp. 239-304. Pergamon Press, Oxford, 1981
Title system model SystemModel 2013-03-22 18:33:34 2013-03-22 18:33:34 camillio (22337) camillio (22337) 6 camillio (22337) Definition msc 93E03