# Documentation

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# 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` p`i. 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

`${\underset{¯}{p}}_{j}\le {p}_{j}\le {\overline{p}}_{j}$`

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 ${\underset{¯}{p}}_{j}$ and ${\overline{p}}_{j}$ 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 ${\underset{¯}{\nu }}_{j}$ and ${\overline{\nu }}_{j}$ on $\frac{d{p}_{j}}{dt}$:

`${\underset{¯}{\nu }}_{j}\le \frac{d{p}_{j}}{dt}\le {\overline{\nu }}_{j}$`

Set ${\underset{¯}{\nu }}_{j}$ = –`Inf` and ${\overline{\nu }}_{j}$ = `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

Hence, you could also specify p by

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

Parameter box