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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. Like their numeric (that is, not uncertain) counterpart, the ss model object, you can build them from state-space matrices using the ss command. When one or more of the state-space matrices contain uncertain elements (also called uncertain Control Design Blocks), the result is a uss model object.

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. When you use these commands to return data, however, they operate on the nominal value of the system only.

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

expand all

ussUncertain state-space model
urealCreate uncertain real parameter
umatCreate uncertain matrix
ucomplexCreate uncertain complex parameter
ucomplexmCreate uncertain complex matrix
ultidynCreate uncertain linear time-invariant object
ufrdUncertain frequency response data model
randatomGenerate random uncertain atom objects
randumatGenerate random uncertain umat objects
randussGenerate stable, random uss objects
getNominalNominal value of uncertain model
actual2normalizedTransform actual values to normalized values
normalized2actualConvert value for atom in normalized coordinates to corresponding actual value
getLimitsValidity range for uncertain real (ureal) parameters
simplifySimplify representation of uncertain object
isuncertainCheck whether argument is uncertain class type
lftdataDecompose uncertain objects into fixed certain and normalized uncertain parts
ltiarray2ussCompute uncertain system bounding given LTI ss array
ucoverFit an uncertain model to set of LTI responses

Topics

Uncertain Models

Introduction to Uncertain Elements

Uncertain elements are the building blocks for representing systems with uncertainty.

Create Models of Uncertain Systems

Represent uncertain parameters and unmodeled dynamics in linear time-invariant models.

Uncertain Real Parameters

Represent real-valued system parameters whose values are uncertain.

Uncertain LTI Dynamics Elements

Represent unknown linear time-invariant dynamics whose only known attributes are bounds on the frequency response.

Uncertain Matrices

Represent matrices whose entries include uncertain values.

Uncertain State-Space Models

Represent linear systems with uncertain state-space matrices or uncertain linear dynamics.

Uncertain Complex Parameters and Matrices

Represent complex-valued uncertain parameters.

Create Uncertain Frequency Response Data Models

Represent a dynamic system as uncertain frequency response data.

Systems with Unmodeled Dynamics

Represent completely unknown, multivariable, time-varying nonlinear systems.

Uncertain Model Interconnections

Interconnect models that include systems with uncertain parameters or dynamics.

System with Uncertain Parameters

Build a closed-loop system with uncertain parameters.

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? (Control System Toolbox)

Model objects represent linear systems as specialized data containers that encapsulate model data and attributes in a structured way.

Types of Model Objects (Control System Toolbox)

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 (Control System Toolbox)

Represent systems that have internal dynamics or memory of past states, such as integrators, delays, transfer functions, and state-space models.

Static Models (Control System Toolbox)

Represent static input/output relationships, including tunable or uncertain parameters and arrays.

Generalized Models (Control System Toolbox)

Generalized models represent systems having a mixture of fixed coefficients and tunable or uncertain coefficients.

Control System Modeling with Model Objects (Control System Toolbox)

Model objects can represent components such as the plant, actuators, sensors, or controllers. You connect model objects to build aggregate models that represent the combined response of multiple elements.

Featured Examples