On the destabilizing effect of cross-coupling in decentralized adaptive control (Q1058497)

The stability of square multivariable linear time-invariant (LTI) systems coupled with an adaptive controller for which the process cross-coupling terms have been neglected is studied in this paper. Our aim is to find conditions over the reference signals richness and the process transfer matrix frequency response such that, for sufficiently small adaptation rates, the stability of the adaptive system is insured. It is shown that if the adaptive system without interconnections is stable then stability of the overall system is preserved if either: (1) The frequency bands of the reference signals are non-overlapping. (2) When there is a spectrum overlap each output of the LTI system to input signals in this spectrum has an average energy where the contribution from its corresponding input is larger than the one due to the other inputs. Global results are obtained for a simple single-parameter adaptation scheme. The extension to general adaptive controllers is straightforward in a local context.