Disturbance decoupling problems via dynamic output feedback

Abstract

Abstruct-This paper considers the disturbance decoupling problems, with or without internal stability and pole placement, via dynamic output feedback using polynomial and rational matrix techniques. We show that in all three problems considered, the central solvability condition can be expressed as a two-sided matching problem A = BXC, where A , B, and Care the polynomialsystem mutrices of certain natural subsystems of the system model and X is to be determined over various subrings of the rational functions. This matching problem can in turn be reduced to certain appropriate zero-cuncellution conditions on the polynomial system matrices A , B, and C.

Disturbance decoupling and robustness of stability

“…It is well known [13] that DDIS is solvable if and only if the pair (A, B) is stabilizable, (C, A) is detectable and the linear matrix equation…”

“…Later, the problem has been solved by dynamic measurement feedback and under the additional condition of closed loop stability. See for instance [16,10,20,13] and the references therein. These studies basically concentrate on the solvability of the problem for a given set of system parameters.…”

The fixed poles of the disturbance decoupling problem and almost stability subspace $\mathcal V^\star_{b,g}({\rm ker}(C))$

“…The disturbance decoupling problem by state feedback and measurement feedback were solved in [4] and [15], respectively. The disturbance decoupling problem by state feedback and measurement feedback with stability or pole placement were, respectively, solved in [10], [20] and [19]. A detailed description of the different results and the geometric theory for all these problems is given in [23].…”