ACHIEVING DIAGONAL INTERACTOR MATRIX FOR MULTIVARIABLE LINEAR-SYSTEMSWITH UNCERTAIN PARAMETERS

The notion of interactor matrix or equivalently the Hermite normal for m, is a generalization of relative degree to multivariable systems, an d is crucial in problems such as decoupling, inverse dynamics, and ada ptive control. In order for a system to be input-output decoupled usin g static state feedback, the existence of a diagonal interactor matrix must first be established. For a multivariable linear system which do es not have a diagonal interactor matrix, dynamic precompensation or d ynamic state feedback is required for achieving a diagonal interactor matrix for the compensated system. Such precompensation often depends on the parameters of system, and is thus difficult to implement with a ccuracy when the system is subject to parameter uncertainty. In this p aper we characterize a class of linear systems which can be precompens ated to achieve a diagonal interactor matrix without the exact knowled ge of the system parameters. More precisely, we present necessary and sufficient conditions on the transfer matrix of the system under which there exists a diagonal dynamic precompensator such that the compensa ted system has a diagonal interactor matrix. These conditions are asso ciated with the so-called (non)generic singularity of certain matrix r elated to the system structure but independent of the system parameter s. The result of this paper is expected to be useful in robust and ada ptive designs.