# Observability

In control theory, observability is a measure of how well internal states of a system can be inferred from knowledge of its external outputs. The observability and controllability of a linear system are mathematical duals. The concept of observability was introduced by Hungarian-American engineer Rudolf E. Kálmán for linear dynamic systems. A dynamical system designed to estimate the state of a system from measurements of the outputs is called a state observer or simply an observer for that system.

Consider a physical system modeled in state-space representation. A system is said to be observable if, for any possible evolution of state and control vectors, the current state can be estimated using only the information from outputs (physically, this generally corresponds to information obtained by sensors). In other words, one can determine the behavior of the entire system from the system's outputs. On the other hand, if the system is not observable, there are state trajectories that are not distinguishable by only measuring the outputs.

from Observability - Wikipedia

This topic includes the following resources and journeys:

Filters
5 items

## State Space, Part 3: A Conceptual Approach to Controllability and Observabil...

13 min
Beginner
Video
Theory

This video helps you answer two really important questions that come up in control systems engineering: Is your system controllable? And is it observable? Assuming you have a good linear...

See More

## The Institute for Systems Theory and Automatic Control MATLAB Apps

Intermediate
App
Theory

The Institute for Systems Theory and Automatic Control offers 5 Matlab Apps on the topics of the Nyquist Criterion, Robustness and Stability, Loopshaping, Controllability and Observability...

See More

## Control Bootcamp: Observability

8 min
Beginner
Video
Theory

This video explores the observability of a linear system, namely the ability to estimate the full state "x(t)" from a time-history of limited output measurements "y(t)".

See More

## Control Bootcamp: Observability Example in Matlab (Part 2)

11 min
Beginner
Video
Application

This video continues to explore observability in Matlab on the example system of an inverted pendulum on a cart. We look at the observability Gramian.

See More

## Control Bootcamp: Observability Example in Matlab

8 min
Beginner
Video
Application

This video explores observability in Matlab on the example system of an inverted pendulum on a cart.

See More