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.

**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.

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.

Represent matrices whose entries include uncertain values.

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.

Access the normalized LFT representation underlying uncertain models.

**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.