Glover Problem B Part 3

Step 3 is just like steps 1 and 2, except we now have three more assumptions to add to the starting relations. We set P33 and its transpose equal to 2, and we set the inverse of P33 and its transpose equal to 1/2. Then we set P23 and its transpose equal to zero. All of this is done in the file problem2.step3.m.

In this step the NCProcess command creates a spreadsheet file called ``Banswer3.dvi''. As usual, we only need to concentrate on the intersting categories. The first two categories involve P12 and its transpose.

The two equations in the P12 category tell us that P12 times A11 transpose to any power, times C1 transpose is zero.

The expressions with unknown variables

and knowns

The expressions with unknown variables

and knowns

The first two equations in the P12 transpose category give a similar result for P12 transpose. If we make certain assumptions about controlability, then we can prove that P12 and its transpose are equal to zero.

The next two categories tell us about the last two elements of the P matrix, P11 and P22.

The expressions with unknown variables

and knowns

The first equation in the above category indicates that perhaps P11 equals

. The other equations in this category give more evidence that this is the case. Remember, that we can run for more iterations and generate equations like this of as high of a degree as we please. Again, we would need to make some sort of assumption about controlability before we could prove that P11 equals

, but the NCProcess does generate what we would need to prove it rigorously.

The expressions with unknown variables

and knowns