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Concept of an LTI Array

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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

What is an LTI Array?

LTI arrays are arrays that store an LTI models as one element in the array. Since an array in MATLAB technical computing software can be treated as a single variable, so can an LTI array. This means that you can operate on, say, 100 LTI models by one operations on a single variable—making LTI arrays a powerful tool if you have large numbers of LTI models to consider in your analysis and design process.

Because LTI arrays are multidimensional in nature, there is a large set of topics that relate to them. This section discusses these topics:

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When to Use an LTI Array

In many applications, it is useful to consider collections of linear, time invariant (LTI) models. For example, you may want to consider a model with a single parameter that varies, such as

sys1 = tf(1, [1 1 1]);
sys2 = tf(1, [1 1 2]);
sys3 = tf(1, [1 1 3]);

and so on. A convenient way to store and analyze a collection like this is to use LTI arrays. Continuing this example, you can create this LTI array and store all three transfer functions in one variable.

sys_ltia = stack(1, sys1, sys2, sys3);

You can use the LTI array sys_ltia just like you would use, for example, sys1.

You can use LTI arrays to collect a set of LTI models into a single MATLAB variable. You then use this variable to manipulate or analyze the entire collection of models in a vectorized fashion. You access the individual models in the collection through indexing rather than by individual model names.

LTI arrays extend the concept of single LTI models in a similar way to how multidimensional arrays extend two-dimensional matrices in the MATLAB technical computing environment (see Multidimensional Arrays in the MATLAB documentation).

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When to Collect a Set of Models in an LTI Array

You can use LTI arrays to represent

• A set of LTI models arising from the linearization of a nonlinear system at several operating points

• A collection of transfer functions that depend on one or more parameters

• A set of LTI models arising from several system identification experiments applied to one plant

• A set of gain-scheduled LTI controllers

• A list of LTI models you want to collect together under the same name

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Restrictions for LTI Models Collected in an Array

For each model in an LTI array, the following properties must be the same:

• The number of inputs and outputs

• The sample time, for discrete-time models

• The I/O names and I/O groups

  Note   You cannot specify Simulink LTI blocks with LTI arrays.

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Where to Find Information on LTI Arrays

The next two sections give examples that illustrate how to visualize an LTI array, its dimensions, and size. To read about how to build an LTI array, go to Building LTI Arrays. The remainder of the chapter is devoted to indexing and operations on LTI arrays. You can also apply the Control System Toolbox analysis functions to LTI arrays. See Model Analysis Tools for more information on these functions. You can also view response plots of LTI arrays with the LTI Viewer.

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Visualizing LTI Arrays

To visualize the concept of an LTI array, consider the set of five transfer function models shown below. In this example, each model has two inputs and two outputs. They differ by parameter variations in the individual model components.

Five LTI Models to be Collected in an LTI Array

An LTI Array Containing These Five Models

Just as you might collect a set of two-by-two matrices in a multidimensional array, you can collect this set of five transfer function models as a list in an LTI array under one variable name, say, sys. Each element of the LTI array is an LTI model.

Individual models in the LTI array sys are accessed via indexing. The general form for the syntax you use to access data in an LTI array is

For example, you can access the third model in sys with sys(:,:,3). The following illustrates how you can use indexing to select models or their components from sys.

Using Indices to Select Models and Their Components

See Concept of an LTI Array for more information on indexing.

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Higher Dimensional Arrays of LTI Models

You can also collect a set of models in a two-dimensional array. The following diagram illustrates a 2-by-3 array of six, two-output, one-input models called m2d.

m2d: A 2-by-3 Array of Two-Output, One-Input Models

More generally, you can organize models into a 3-D or higher-dimensional array, in much the same way you arrange numerical data into multidimensional arrays (see Multidimensional Arrays in the MATLAB documentation).

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Arrays of LTI Models

Dimensions, Size, and Shape of an LTI Array

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