Uncertain Models

Uncertain state-space and frequency response models

Uncertain state-space (uss) models are linear systems with uncertain state-space matrices, uncertain linear dynamics, or both. Most functions that work on numeric LTI models also work on uss models. These include model interconnection functions such as connect and feedback, and linear analysis functions such as bode and stepinfo. Some functions that generate plots, such as bode and step, plot random samples of the uncertain model to give you a sense of the distribution of uncertain dynamics.

In addition, you can use functions such as robstab and wcgain to perform robustness and worst-case analysis of uncertain systems represented by uss models. You can also use tuning functions such as systune for robust controller tuning.

Functions

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Uncertain Elements and Models

`uss`	Uncertain state-space model
`ureal`	Uncertain real parameter
`ucomplex`	Create uncertain complex parameter
`ucomplexm`	Create uncertain complex matrix
`ultidyn`	Uncertain linear time-invariant dynamics
`umargin`	Model gain and phase uncertainty (Since R2020a)
`umat`	Create uncertain matrix
`ufrd`	Uncertain frequency response data model
`ucover`	Fit uncertain model to set of LTI responses
`randatom`	Generate random uncertain `atom` objects
`randumat`	Generate random uncertain `umat` objects
`randuss`	Generate stable, random `uss` objects
`diag`	Diagonal uncertain matrices; diagonals of an uncertain matrix

Uncertainty Values and Model Attributes

`getNominal`	Nominal value of uncertain model
`uscale`	Scale uncertainty of block or system (Since R2020a)
`plot (umargin)`	Visualize gain and phase uncertainty of a `umargin` block (Since R2020a)
`actual2normalized`	Transform actual values to normalized values
`normalized2actual`	Convert value for atom in normalized coordinates to corresponding actual value
`getLimits`	Validity range for uncertain real (`ureal`) parameters
`simplify`	Simplify representation of uncertain object
`isuncertain`	Check whether argument is uncertain class type
`lftdata`	Decompose uncertain objects into fixed certain and normalized uncertain parts
`ltiarray2uss`	Compute uncertain system bounding given LTI `ss` array

Topics

Uncertain Models

Introduction to Uncertain Elements

Uncertain elements are the building blocks for representing systems with uncertainty.
- Uncertain Real Parameters
- Uncertain LTI Dynamics Elements
- Uncertain Gain and Phase
- Uncertain Matrices
- Uncertain Complex Parameters and Matrices
- Systems with Unmodeled Dynamics
Create Models of Uncertain Systems

Represent uncertain parameters and unmodeled dynamics in linear time-invariant models.
Uncertain Model Interconnections
Interconnect models that include systems with uncertain parameters or dynamics.
Simplifying Representation of Uncertain Objects
Simplify uncertain models built up from uncertain elements to ensure that the internal representation of the model is minimal.
Decomposing Uncertain Objects
Access the normalized LFT representation underlying uncertain models.

Model Object Basics

What Are Model Objects?
Model objects represent linear systems as specialized data containers that encapsulate model data and attributes in a structured way.
Types of Model Objects

Model object types include numeric models, for representing systems with fixed coefficients, and generalized models for systems with tunable or uncertain coefficients.
- Dynamic System Models
- Static Models
- Generalized Models
Control System Modeling with Model Objects
Build models that represent your control system using model objects.

Related Information

Working with Parameter Uncertainty

Featured Examples

Building and Manipulating Uncertain Models

Use Robust Control Toolbox™ software to build uncertain state-space models and analyze the robustness of feedback control systems with uncertain elements.

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Model Gain and Phase Uncertainty in Feedback Loops

Model gain and phase uncertainty in feedback loops and check for robust stability against such uncertainty.

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Modeling a Family of Responses as an Uncertain System

Use ucover to fit an uncertain model to a set of frequency responses representative of the system variability. You can also use it to reduce the complexity of an existing uncertain model.

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