Contents

Index

• Getting Started

• Creating and Manipulating Models

• Linear, Time-Invariant Models

Supported Model Types

LTI Model Formats

Examples of Creating LTI Models

Using LTI Models

Precedence Rules

Viewing LTI Systems as Matrices

LTI Command Summary

• Creating LTI Models

Transfer Function Models

Zero-Pole-Gain Models

State-Space Models

Descriptor State-Space Models

Frequency Response Data (FRD) Models

Creating Discrete-Time Models

• LTI Properties

What are LTI Properties?

Generic LTI Properties

Model-Specific Properties

Setting LTI Properties

Accessing Property Values Using get

Direct Property Referencing Using Dot Notation

Additional Insight into LTI Properties

• Model Conversion

Available Model Formats

Explicit Conversion

Automatic Conversion

Caution About Model Conversions

• Time Delays

Supported Types of Delays

Available Properties for Modeling Delays

Input and Output Delays

Specifying I/O Delays in MIMO Models

Internal Delays

Analyzing Systems With Delays

Eliminating Time Delays: Padé Approximation

Sensitivity Analysis

Specifying Delays in Discrete-Time Models

Functions That Support Internal Time Delays

Functions That Do Not Support Internal Time Delays

Inside Time Delay Models

Simulink Block for LTI Systems

• Operations on LTI Models

Precedence and Property Inheritance

• Extracting and Modifying Subsystems

What is a Subsystem?

Basic Subsystem Concepts

Referencing FRD Models Through Frequencies

Referencing Channels by Name

Resizing LTI Systems

• Arithmetic Operations on LTI Models

Supported Arithmetic Operations

Addition and Subtraction

Inversion and Related Operations

Pertransposition

• Model Interconnection Functions

Supported Interconnection Functions

Concatenation of LTI Models

Feedback and Other Interconnection Functions

• Continuous/Discrete Conversions of LTI Models

Supported Conversion Functions and Methods

Zero-Order Hold

First-Order Hold

Impulse Invariance

Tustin Approximation

Tustin with Frequency Prewarping

Matched Poles and Zeros

Discretization of Systems with Delays

• Resampling of Discrete-Time Models

Available Commands for Resampling Discrete-Time Models

Example of Resampling a Discrete-Time Model

• Model Analysis Tools

General Model Characteristics

State-Space Realizations

• Arrays of LTI Models

• Concept of an LTI Array

What is an LTI Array?

When to Use an LTI Array

When to Collect a Set of Models in an LTI Array

Restrictions for LTI Models Collected in an Array

Where to Find Information on LTI Arrays

Visualizing LTI Arrays

Higher Dimensional Arrays of LTI Models

• Dimensions, Size, and Shape of an LTI Array

I/O and Array Dimensions of LTI Arrays

Accessing the Dimensions of an LTI Array Using size and ndims

Using reshape to Rearrange an LTI Array

• Building LTI Arrays

Ways to Build LTI Arrays

Building LTI Arrays Using for Loops

Building LTI Arrays Using the stack Function

Building LTI Arrays Using tf, zpk, ss, and frd

Generating Random LTI Arrays Using rss

• Indexing into LTI Arrays

When to Index into LTI Arrays

Organization of Indices

Note on Indexing into LTI Arrays of FRD Models

Accessing Particular Models in an LTI Array

Extracting LTI Arrays of Subsystems

Reassigning Parts of an LTI Array

Deleting Parts of an LTI Array

• Operations on LTI Arrays

Supported Operations on LTI Arrays

Example: Addition of Two LTI Arrays

Dimension Requirements

Special Cases for Operations on LTI Arrays

Other Operations on LTI Arrays

• Customization

• Control System Toolbox Design Case Studies

• Control System Toolbox Reliable Computations

• Using the SISO Design Tool and the LTI Viewer

• Release Notes

Learn more about Control System Toolbox

Creating and Manipulating Models

LTI Models	Introduces key concepts about the MATLAB representation of linear, time-invariant (LTI) models, including LTI objects, precedence rules for operations, and an analogy between LTI systems and matrices. It also summarizes the basic commands you can use on LTI objects.
Operations on LTI Models	How to perform basic matrix operations such as addition, multiplication, or concatenation on LTI models. This chapter also discusses discretization methods.
Model Analysis Tools	Discusses functions that display model characteristics, such as input/output pairs, analyze model dynamics, such as pole and zero locations, and transform state-space models into canonical representations.
Arrays of LTI Models	Describes the LTI Array, which you can use to collect a set of LTI models into a single MATLAB variable. You can then use this single variable to manipulate or analyze the entire collection of models.

LTI Models

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