A new tuning method for robust decentralised PI controllers is given. The c
ontroller tunings are obtained by minimising a robust performance criterion
. The cost function to be minimised is derived from the standard mu-synthes
is criterion and it takes into account the process uncertainty and the desi
red performance. A constraint on the variations of the controller outputs c
an also be added to the performance criterion. The two options, with and wi
thout a constraint, respect the specifications in a minimal way to limit th
e controller output variations obtained from the standard mu-synthesis crit
erion. These two options and the standard mu-synthesis criterion are compar
ed on an ill-conditioned two-input two-output (TITO) process example. The g
eneralised step response for TITO processes is used to analyse the time beh
aviour of closed-loop systems.