pvec

Specify range and rate of variation of uncertain or time-varying parameters

Syntax

pv = pvec('box',range,rates)
pv = pvec('pol',vertices)

Description

pvec is used in conjunction with psys to specify parameter-dependent systems. Such systems are parametrized by a vector p = (p1, . . ., pn) of uncertain or time-varying real parameters pi. The function pvec defines the range of values and the rates of variation of these parameters.

The type 'box' corresponds to independent parameters ranging in intervals

p¯jpjp¯j

The parameter vector p then takes values in a hyperrectangle of Rn called the parameter box. The second argument range is an n-by-2 matrix that stacks up the extremal values p¯j and p¯j of each pj. If the third argument rates is omitted, all parameters are assumed time-invariant. Otherwise, rates is also an n-by-2 matrix and its j-th row specifies lower and upper bounds ν¯j and ν¯j on dpjdt:

ν¯jdpjdtν¯j

Set ν¯j = –Inf and ν¯j = Inf if pj(t) can vary arbitrarily fast or discontinuously.

The type 'pol' corresponds to parameter vectors p ranging in a polytope of the parameter space Rn. This polytope is defined by a set of vertices V1, . . ., Vn corresponding to "extremal" values of the vector p. Such parameter vectors are declared by the command

pv = pvec('pol',[v1,v2, . . ., vn])

where the second argument is the concatenation of the vectors v1,...,vn.

The output argument pv is a structured matrix storing the parameter vector description. Use pvinfo to read the contents of pv.

Examples

Consider a problem with two time-invariant parameters

p1 ∊ [–1, 2], p2 ∊ [20, 50]

The corresponding parameter vector p = (p1, p2) is specified by

pv = pvec('box',[-1 2;20 50])

Alternatively, this vector can be regarded as taking values in the rectangle drawn in the following figure. The four corners of this rectangle are the four vectors

v1=(120), v2=(150), v3=(220), v4=(250)

Hence, you could also specify p by

pv = pvec('pol',[v1,v2,v3,v4])

Parameter box

See Also

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