Mu Analysis and Synthesis Toolbox

Reduce the state dimension of a SYSTEM matrix

Syntax
sysout = sresid(sys,ord)

sysout = strunc(sys,ord)

Description
sresid residualizes the last states of a SYSTEM matrix sys. sresid accounts for the DC contribution of the last columns and rows of the SYSTEM A matrix and the corresponding rows and columns of B and C. sresid assumes that the SYSTEM matrix is ordered so that the last states are to be residualized. If the orignal SYSTEM matrix is partitioned as

with A₁₁ of size ord x ord, then the command

• sysout = sresid(sys,ord)
  

strunc truncates the states of the input system matrix sys, to a system with state dimension equal to ord. strunc can be used in conjunction with the model reduction routines sysbal and hankmr.

The resulting SYSTEM output matrix is

• sysout = pss2sys ([A_11 B_1; C_1 D]);
  

Examples
A two input, one output, four state SYSTEM is reduced down to a two input, one output, two state SYSTEM via sresid and strunc. The only difference between the two reduced-order systems is the value of their D matrices.

• seesys(sys)
  -1.2e-01   0.0e+00   0.0e+00   0.0e+00 | 9.le-01   5.2e-01
   0.0e+00  -3.2e-01   0.0e+00   0.0e+00 | 6.le-02   3.2e-01
   0.0e+00   0.0e+00  -4.3e+00   0.0e+00 | 9.le-01   9.9e-01
   0.0e+00   0.0e+00   0.0e+00  -9.9e+01 | 5.le-01   4.9e-01
  ---------------------------------------|-------------------
   2.7e-01   9.le-02   9.5e-01   7.4e-02 | 0.0e+00   0.0e+00
  
  
  sys_strunc = strunc(sys,3);
  seesys(sys_strunc)
  -1.2e-01    0.0e+00   0.0e+00  |  9.le-01   5.2e-01
   0.0e+00   -3.2e-01   0.0e+00  |  6.le-02   3.2e-01
   0.0e+00    0.0e+00  -4.3e+00  |  9.le-01   9.9e-01
  -------------------------------|---------------------
   2.7e-01    9.le-02   9.5e-01  |  0.0e+00   0.0e+00
  
  sys_resid = sresid(sys,3)
  seesys(sys_resid)
  
  -1.2e-01   0.0e+00   0.0e+00  |  9.le-01   5.2e-01
   0.0e+00  -3.2e-01   0.0e+00  |  6.le-02   3.2e-01
   0.0e+00   0.0e+00  -4.3e+00  |  9.le-01   9.9e-01
  ------------------------------|--------------------
   2.7e-01   9.le-02   9.5e-01  |  3.8e-04   3.7e-04
  
  sysstrunc = strunc(sys,3); seesys(sysstrunc)
  sysresid = sresid(sys,3); seesys(sysresid)
  

See Also
rifd, statecc, strans

srelbal, sfrwtbal, sfrwtbld, sncfbal, sdecomp

starp