In control engineering, a state-space representation is a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations or difference equations. State variables are variables whose values evolve over time in a way that depends on the values they have at any given time and on the externally imposed values of input variables. Output variables’ values depend on the values of the state variables.

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# State Space Representation

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## State Space, Part 1: Introduction to State-Space Equations

Mathworks - Brian Douglas

14 min

Beginner

Video

Theory

Let’s introduce the state-space equations, the model representation of choice for modern control. This video is the first in a series on MIMO control and will provide some intuition around...

See More## State Space Representation of Differential Equations

Christopher Lum

69 min

Beginner

Video

Theory

In this video we show how to represent differential equations (either linear or non-linear) in state space form. This is useful as it allows us to combine an...

See More## State Space to Transfer Function

Christopher Lum

48 min

Beginner

Video

Theory

In this video we show how to transform a linear state space representation of a dynamic system to an equivalent transfer function representation. We will de...

See More## State Space in Process Control

Vincent Stevenson

10 min

Beginner

Video

Theory

An overview on how we can derive a state space model from a given set of state variables and inputs, as well as an intro to deviation variables. This is part...

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