Linearisert

Linearisert is a term used in technical contexts to denote the act of linearizing a nonlinear model or function around a reference operating point. In this sense, it refers to creating a linear approximation that preserves essential behavior of the system within a limited region of the state space.

The standard method for linearisert involves a first‑order Taylor expansion about a chosen operating point. For a nonlinear system described by f(x, u), the linearized model typically takes the form dx/dt ≈ A x + B u + c, where A and B are the Jacobian matrices of partial derivatives with respect to x and u evaluated at the operating point, and c accounts for constant terms. In discrete time, x_{k+1} ≈ A x_k + B u_k + c. The resulting linear model can then be analyzed or designed using linear control theory, estimation, or frequency-domain methods.

Linearisert is widely used in control engineering, robotics, electronics, and economics to enable small-signal analysis, stability assessment, controller design (for example, with LQR or MPC), and performance evaluation around a nominal operating point. It is understood as a local approximation; the accuracy of the linear model degrades as the system moves farther from the reference point or when nonlinear effects dominate.

Etymology-wise, linearisert is related to the standard English term linearize and may appear in German‑language sources in a conjugated form. Related concepts include linearization, the Jacobian, and Taylor series expansion.