Automatica, Vol.33, No.5, 805-820, 1997
Unfalsified Plant-Model Parameterization from Closed-Loop Experimental-Data
The problem of parameterizing all unfalsified plant models from closed-loop time-domain identification experimental data is investigated in this paper. The assumed a priori plant information is an upper bound of the L-x norm and the number of the unstable poles of its transfer function. Moreover, it is assumed that magnitude bounds of the disturbances that perturb the closed-loop system have been supplied. Under the condition that the stabilizing controller is known, it is shown that all the unfalsified plant transfer functions can be parameterized by a linear fractional transformation of a fixed transfer-function matrix and an L-infinity-norm-bounded, structure-fixed but uncertain transfer-function matrix. These results are very similar to those when plant open-loop time-domain identification experimental data are supplied. However, further efforts are still needed in order to apply these results to robust controller design. This results mainly from the computational complexity and the high dimensions of the transfer-function matrices involved in the parameterization.