Almost Disturbance Decoupling: Static state feedback solutions with maximal pole assignment

This paper is concerned with maximal pole placement solutions for the Almost Disturbance Decoupling Problem (ADDP) by static state feedback. It is shown that, when solving ADDP by means of high gain state feedback, always are present some fixed finite poles and poles close to infinity in the closed loop system, which can not be freely assigned. A class of “optimal” geometric subspaces with which maximal complementary pole placement can be achieved is characterized. A reliable construction algorithm for such an optimal geometric subspace (resp. the state feedback solution) is also proposed for a particular class of linear systems. An example is proposed to illustrate our contributions.

[1]  Elena Zattoni.  Filtering theory with applications to fault detection, isolation, and estimation. A. Saberi, A. A. Stoorvogel, P. Sannuti, Birkhäuser, Boston, 2007. No. of pages: 723. ISBN 978‐0‐8176‐4301‐0 , 2009 .

[2]  Johannes Schumacher,et al.  Almost stabilizability subspaces and high gain feedback , 1984 .

[3]  G. Basile,et al.  Controlled and conditioned invariants in linear system theory , 1992 .

[4]  H. Trentelman.  Almost invariant subspaces and high gain feedback , 1985 .

[5]  J. Pearson.  Linear multivariable control, a geometric approach , 1977 .

[6]  D. Chu.  The fixed poles of the disturbance decoupling problem and almost stability subspace V , 2003 .

[7]  H. Trentelman,et al.  On the assignability of infinite root loci in almost disturbance decoupling , 1983 .

[8]  W. Wonham.  Linear Multivariable Control: A Geometric Approach , 1974 .

[9]  J. Willems.  Almost invariant subspaces: An approach to high gain feedback design--Part II: Almost conditionally invariant subspaces , 1981 .

[10]  Delin Chu.  The fixed poles of the disturbance decoupling problem and almost stability subspace $\mathcal V^\star_{b,g}({\rm ker}(C))$ , 2003, Numerische Mathematik.

[11]  M. Malabre,et al.  Almost Self-Bounded Controlled-Invariant Subspaces and Almost Disturbance Decoupling , 2008 .

[12]  Michel Malabre,et al.  On the fixed poles for disturbance rejection , 1997, Autom..

[13]  Jan Willems,et al.  Almost invariant subspaces: An approach to high gain feedback design , 1981, 1981 20th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[14]  Ali Saberi,et al.  Filtering theory , 2007 .

[15]  A complement about almost controllability subspaces , 1983 .

[16]  Michel Malabre,et al.  Almost disturbance decoupling and pole placement , 2009, Autom..