TITLE:
Explicit Determination of State Feedback Matrices
AUTHORS:
Omar Moh’d El-Basheer El-Ghezawi
KEYWORDS:
State Feedback, Eigenstructure Assignment, Pole Placement, Explicit Methods
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.5 No.7,
June
2,
2015
ABSTRACT: Methods
which calculate state feedback matrices explicitly for uncontrollable systems
are considered in this paper. They are based on the well-known method of the
entire eigenstructure assignment. The use of a particular similarity
transformation exposes certain intrinsic properties of the closed loop w-eigenvectors
together with their companion z-vectors. The methods are extended further to
deal with multi-input control systems. Existence of eigenvectors solution is established.
A differentiation property of the z-vectors is proved for the repeated eigenvalues
assignment case. Two examples are worked out in detail.