# Linearization

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## linearization

[‚lin·ē·ər·ə′zā·shən] (control systems)

The modification of a system so that its outputs are approximately linear functions of its inputs, in order to facilitate analysis of the system.

The mathematical approximation of a nonlinear system, whose departures from linearity are small, by a linear system corresponding to small changes in the variables about their average values.

(cell and molecular biology)

Conversion of a circular deoxyribonucleic acid molecule into a linear molecule.

## Linearization

a method of approximate representation of closed nonlinear systems in which the study of a nonlinear system is replaced by analysis of a linear system that is equivalent in some sense to the original system. Linearization methods are limited—that is, the equivalence of the original, nonlinear system and its linear approximation is valid only for a certain “mode” of system operation. If the system moves from one operational mode to another, the linearized model must be changed correspondingly. Methods of linearization may be used to ascertain many qualitative and, in particular, quantitative properties of a nonlinear system.

### REFERENCES

Popov, E. P., and I. P. Pal’tov.*Priblizhennye metody issledovaniia nelineinykh avtomaticheskikh sistem.*Moscow, 1960.

Pervozvanskii, A. A.

*Sluchainye protsessy v nelineinykh avtomaticheskikh sistemakh.*Moscow, 1962.

*Osnovy avtomaticheskogo upravleniia.*Edited by V. S. Pugachev. Moscow, 1963.