Robust Control Toolbox™

Create uncertain linear time-invariant object

Syntax

• H = ultidyn('Name',iosize) 
  H = 
  ultidyn('Name',iosize,'Property1',Value1,'Property2',Value2,...
  ) 
  

Description

H = ultidyn('Name',iosize) creates an uncertain linear, time-invariant objects are used to represent unknown dynamic objects whose only known attributes are bounds on their frequency response. Uncertain linear, time-invariant objects have a name (the Name property), and an input/output size (ioSize property).

The property Type is 'GainBounded' (default) or 'PositiveReal', and describes in what form the knowledge about the object's frequency response is specified.

• If Type is 'GainBounded', then the knowledge is an upper bound on the magnitude (i.e., absolute value), namely abs(H)<= Bound at all frequencies. The matrix generalization of this is ||H||<= Bound.
• If Type is 'PositiveReal' then the knowledge is a lower bound on the real part, namely Real(H) >= Bound at all frequencies. The matrix generalization of this is H+H' >= 2*Bound

The property Bound is a real, scalar that quantifies the bound on the frequency response of the uncertain object as described above.

Trailing Property/Value pairs are allowed in the construction.

H=ultidyn('name',iosize,'Property1',Value1,'Property2',Value2,...)

The property SampleStateDim is a positive integer, defining the state dimension of random samples of the uncertain object when sampled with usample. The default value is 1.

The property AutoSimplify controls how expressions involving the uncertain matrix are simplified. Its default value is 'basic', which means elementary methods of simplification are applied as operations are completed. Other values for AutoSimplify are 'off'', no simplification performed, and 'full' which applies model-reduction-like techniques to the uncertain object.

Example

Example 1

Create an ultidyn object with internal name 'H', dimensions 2-by-3, norm bounded by 7.

• H = ultidyn('H',[2 3],'Bound',7) 
  Uncertain GainBounded LTI Dynamics: Name H, 2x3, Gain Bound = 7 
  

Example 2

Create a scalar ultidyn object with an internal name 'B', whose frequency response has a real part greater than 2.5. Change the SampleStateDim to 5, and plot the Nyquist plot of 30 random samples.

• B = ultidyn('B',[1 1],'Type','PositiveReal','Bound',2.5) 
  Uncertain PositiveReal LTI Dynamics: Name B, 1x1, M+M' >= 2*(2.5) 
  B.SampleStateDim = 5; 
  nyquist(usample(B,30))
  
  
  

See Also
get         Gets object properties

ureal       Creates an uncertain real parameter

uss         Creates an uncertain LTI system object

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