# What is a linearization model?

## What is a linearization model?

Linearize Simulink models Linearization involves creating a linear approximation of a nonlinear system that is valid in a small region around the operating or trim point, a steady-state condition in which all model states are constant.

**What are state-space models used for?**

State-space models are models that use state variables to describe a system by a set of first-order differential or difference equations, rather than by one or more nth-order differential or difference equations.

### Why do we need linearization?

Linearization can be used to give important information about how the system behaves in the neighborhood of equilibrium points. Typically we learn whether the point is stable or unstable, as well as something about how the system approaches (or moves away from) the equilibrium point.

**What are the limitations of state space model?**

One of the main drawbacks of state space methods is the so-called state explosion problem. For many systems, the state space becomes so large that it cannot be fully constructed. In practice, our present state space tool supports state spaces with up to half a million nodes and one million arcs.

#### Can the formulas for linearizing nonlinear discrete-time state space models be derived?

The formulas for linearizing nonlinear discrete-time state space models are presented without derivation below. They can be derived in the same way as for linearizing nonlinear continuous-time models [1]. In the formulas below it assumed a second order system. I guess it is clear how the formulas can be generalized to higher orders.

**Is it possible to derive second order systems for linearizing nonlinear models?**

They can be derived in the same way as for linearizing nonlinear continuous-time models [1]. In the formulas below it assumed a second order system. I guess it is clear how the formulas can be generalized to higher orders.

## What is the linear model of a system?

The corresponding linear model, which deﬁnes the system’s dynamic behaviour about a speciﬁcoperating point, is ∆x1(k+1) =∂f1 ∂x1

**Is the simplified linearized model a good model for the inverted pendulum?**

Finally, the state space matrix of the simplified linearized model is obtained, which provides a good model basis for the control and Simulation of the inverted pendulum. References