INDEX

Function: pqrdelta

Purpose
Adapts an lfr-object with initial delta-block delta1 so that this block becomes delta2 where delta1 = P delta2 Q + R.

Synopsis

[D11,D12,D21,D22] = pqrdelta(M11,M12,M21,M22,P,Q,R)
[D11,D12,D21,D22] = pqrdelta(SYS1,P,Q,R)

Remarks

  • This function is not expected to be of great interest for standard users of the toolbox. Use preferably ordelta. Its interest is limited to transformations of the delta-block that are not coded in other functions.
  • The output argument cannot be an lfr-object because it is not possible to compute the new block description matrix (matrix blk) from P, Q and from the original one (there are some ambiguous cases). To get an lfr-object, build the new block description matrix blk and use SYS2 = lfr(D11,D12,D21,D22,blk)

Input arguments

M11,M12,M21,M22 or
SYS1 Matrices or lfr-object. ([M11,M12,M21,M22] = lfrdata(SYS1))
P, Q, R Matrices, P : n2 X n1, Q : n1 X n2, R : n2 X n2 where n1 and n2 are respectively the sizes of initial and returned square delta-blocks matrices. (P = 0 or Q = 0 or R = 0 are accepted).

Output arguments

D11, D12, D21, D22 Matrices defining an lfr-object (only blk missing, see the above remark).

See also: ordelta, flup, normlfr

Example

Two real block of order 2 are permuted. First, a random system with 8 states and two real uncertainties repeated 2 times is created. 
   sys1 = rlfr(8,2,4,2,2);
The 3 matrices P, Q and R are defined 
   R = zeros(12,12);
   P = eye(12,12); P(9:12,9:12)=[0 0 1 0;0 0 0 1;1 0 0 0;0 1 0 0];
   Q = P

Q =

     1     0     0     0     0     0     0     0     0     0     0     0
     0     1     0     0     0     0     0     0     0     0     0     0
     0     0     1     0     0     0     0     0     0     0     0     0
     0     0     0     1     0     0     0     0     0     0     0     0
     0     0     0     0     1     0     0     0     0     0     0     0
     0     0     0     0     0     1     0     0     0     0     0     0
     0     0     0     0     0     0     1     0     0     0     0     0
     0     0     0     0     0     0     0     1     0     0     0     0
     0     0     0     0     0     0     0     0     0     0     1     0
     0     0     0     0     0     0     0     0     0     0     0     1
     0     0     0     0     0     0     0     0     1     0     0     0
     0     0     0     0     0     0     0     0     0     1     0     0
The permutation of parameters is performed: 
   [D11,D12,D21,D22] = pqrdelta(sys1,P,Q,R);
   sys2 = lfr(D11,D12,D21,D22,[-8 0;-2 0;-2 0]);