What Is State Space?

A state-space model is commonly used for representing a linear time-invariant (LTI) system. It describes a system with a set of first-order differential or difference equations using inputs, outputs, and state variables. In the absence of these equations, a model of a desired order (or number of states) can be estimated from measured input-output data.

The models are widely used in modern control applications for designing controllers and analyzing system performance in the time domain and frequency domain. The models can be applied to nonlinear systems or systems with non-zero initial conditions. They also provide a convenient way to represent, analyze, and control multi-input/multi-output (MIMO) systems.

For more on control system design, see Control System Toolbox™ and System Identification Toolbox™ for use with MATLAB^®.

Examples and How To

Creation and Analysis | State-Space Models, Part 1 (2:44) - Video
Control Design | State-Space Models, Part 2 (5:57) - Video
Estimating State-Space and Polynomial Models (2:20) - Video
Yaw Damper Design for a 747 Jet Aircraft - Tutorial
State-Space Methods for Controller Design - Carnegie Mellon University Tutorial
Switching Model Representation - Example
Creating Continuous-Time Models - Example

Software Reference

ss - Function
State-Space - Simulink Block
Conversion Between Model Types - Documentation
place - Function
ssest - Function

State-Space Models (2 videos)