On the fixed poles for disturbance rejection

Fixed Poles for Non Minimal Systems: A Geometric Approach

“…C = Id (Identity). Remembering that for the particular case of state feedback, static and dynamic solutions are known to be equivalent (see Emre and Hautus, 1980), this gives an alternative description to the DRSF Fixed Poles characterised in (Malabre et al 1997).…”

A geometric theory for 2-D systems including notions of stabilisability

“…to (18) is such that the pair (X 1 , X 2 ) is asymptotically stable. Since the only degree of freedom here lies in the choice of Ω, which in turn is given by (20), we find that…”

“…Disturbance decoupling with the additional requirement of internal stability was considered by Wonham and Morse in [24], via the introduction of (A, B) stabilisability subspaces. An improved solution to the same problem was subsequently suggested by Basile and Marro in [2], using the concept of self-bounded controlled invariance to avoid eigenspace computation; this permits the maximum number of eigenvalues of the closed-loop to be freely placed, as later shown by Malabre, Martínez-García, and Del-Muro-Cuéllar [18].…”

An optimal geometric solution of almost disturbance decoupling via state feedback with pole placement

“…These fixed poles and infinite poles do not depend on the choice of the control law but precisely on the fact that this particular problem is solvable. The DDP by state feedback with maximal pole placement has been solved by introducing the concept of fixed poles [5], [6] . There has been a large number of research results about ADDP (without considering numerical solutions) in 1980s [7][8][9] .…”