MATLAB Examples

## tcomp(m,N)

```% For a random plant and random measurements, compare the performance of % three methods for updating the polytopic uncertainty set. ```

## Inputs

```% m = the order of the plant % N = the number of time instants ```

## Outputs

```% time = the update time taken by the three methods. % FV = the number of facets and vertices in the updated uncertainty set. % facets_plp = the number of facets as calculated by plp. % facets_fourier = the number of facets as calculated by fourier-motzkin. % z = measurements % num, den = the numerator and denominator of the plant ```

## Size and type of input data

```% m = integer greater than or equal to two. % N = integer number of updates greater than or equal to one. ```

## Size and type of output data

```% time = 3 x N floating point matrix; the first, second and third rows give, respectively, the update times % for the FV algorithm, parametric linear programming and Fourier-Motzkin. % FV = 2 x N integer matrix; the n'th column gives the number of facets and % vertices of the uncertainty set after processing the n'th measurement. % facets_plp = 1 x N integer matrix. % facets_fourier = 1 x N integer matrix. % z = 1 x N row vector of scalars. % num,den = m+1 dimensional row vectors, floating point with den(1)=1, num(1)>0, and num(m+1)den(m+1)<0. ```

## EXAMPLE

``` m=3; N=15; [time,FV,facets_plp,facets_fourier,z,num,den]=tcomp(m,N) ```
```time = Columns 1 through 7 0.0107 0.0103 0.0072 0.0098 0.0105 0.0084 0.0088 0.1755 0.2715 0.3472 0.5950 0.6391 0.8703 1.5082 0.1563 0.1567 0.1661 0.1739 0.2020 0.1995 0.2791 Columns 8 through 14 0.0084 0.0115 0.0108 0.0159 0.0111 0.0533 0.0244 1.8685 1.6741 0.9065 0.3596 0.8769 1.2731 0.3638 0.4420 0.4068 0.4799 0.9881 0.6761 1.8902 0.3408 Column 15 0.0142 1.1524 0.2494 FV = Columns 1 through 13 7 12 19 29 31 35 52 58 57 71 73 77 85 9 17 23 37 41 44 65 76 74 98 100 102 136 Columns 14 through 15 71 48 102 65 facets_plp = Columns 1 through 13 7 12 19 29 31 35 52 58 57 71 73 77 85 Columns 14 through 15 71 48 facets_fourier = Columns 1 through 13 7 12 19 29 31 35 52 58 57 71 73 77 85 Columns 14 through 15 71 45 z = Columns 1 through 7 -3.0990 -4.0485 -9.8880 -6.4152 -1.9985 -11.2384 -16.0291 Columns 8 through 14 -18.5856 -8.6223 7.1430 8.9720 13.6994 4.7325 1.8527 Column 15 14.7248 num = 3.0427 7.5905 -5.0070 -4.0089 den = 1.0000 -0.9801 -0.1217 0.1958 ```