gramOptions

R2026b

Options for the gram function

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Syntax

opt = gramOptions
opt = gramOptions(Name=Value)

Description

opt = gramOptions returns an option set with the default options for gram.

opt = gramOptions(Name=Value) returns an options set with the options specified by one or more name-value arguments.

example

Examples

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Open Live Script

Compute the controllability Gramian of the following state-space model. Focus the computation on the frequency interval with the most energy.

sys = ss([-.1 -1;1 0],[1;0],[0 1],0);

The model contains a peak at 1 rad/s. Use gramOptions to specify an interval around that frequency.

opt = gramOptions(FreqIntervals=[0.8 1.2]);
gc = gram(sys,"c",opt)
gc = 2×2

    4.2132    0.0000
    0.0000    4.2433

Name-Value Arguments

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Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Example: gramOptions(FreqIntervals=[0.8 1.2]) sets a single frequency interval value.

Frequency intervals for computing frequency-limited controllability and observability Gramians, specified as a matrix with two columns. Each row specifies a frequency interval [fmin fmax], where fmin and fmax are nonnegative frequencies, expressed in the frequency unit of the model. For example:

  • To restrict the computation to the range between 3 rad/s and 15 rad/s, assuming the frequency unit of the model is rad/s, set FreqIntervals to [3 15].

  • To restrict the computation to two frequency intervals, 3-15 rad/s and 40-60 rad/s, use [3 15; 40 60].

  • To specify all frequencies below a cutoff frequency fcut, use [0 fcut].

  • To specify all frequencies above the cutoff, use [fcut Inf] in continuous time, or [fcut pi/Ts] in discrete time, where Ts is the sample time of the model.

The default value, [], imposes no frequency limitation and is equivalent to [0 Inf] in continuous time or [0 pi/Ts] in discrete time. However, if you specify a TimeIntervals value other than [], then this limit overrides FreqIntervals = []. If you specify both a TimeIntervals value and a FreqIntervals value, then the computation uses the union of these intervals.

Time intervals for computing time-limited controllability and observability Gramians, specified as a matrix with two columns. Each row specifies a time interval [tmin tmax], where tmin and tmax are nonnegative times, expressed in the time unit of the model. For example:

  • To restrict the computation to the range between 3 s and 15 s, assuming the time unit of the model is seconds, set TimeIntervals to [3 15].

  • To restrict the computation to two time intervals, 3-15 s and 40-60 s, use [3 15; 40 60].

  • To specify all times from zero up to a cutoff time tcut, use [0 tcut]. To specify all times after the cutoff, use [tcut Inf].

The default value, [], imposes no time limitation and is equivalent to [0 Inf]. However, if you specify a FreqIntervals value other than [], then this limit overrides Timeintervals = []. If you specify both a TimeIntervals value and a FreqIntervals value, then the computation uses the union of these intervals.

Output Arguments

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Options for gram, returned as a gramOptions options set. Use opt as the last argument to gram to compute time-limited or frequency-limited Gramians.

Version History

Introduced in R2016a

See Also

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