Reduction of redundant data in the quadratic cost formulation for linear time-variant systems

Time-variant systems represented by pairs of matrices
(A(t), B(t))
and
(\bar{A}(t), \bar{B}(t))
are said to be
F
-equivalent if there exist differentiable matrices
C, G
, and
D
such that
\bar{A}=C^{-1}[(A+BG)- \dot{C}C^{-1}]C, \bar{B} =C^{-1}BD
and
K
-equivalent if
G\equiv 0
. The extent of independent parameters (functions) in the quadratic cost formulation for a linear time-variant system is reported. For the
K
-equivalent class and the
F
- equivalent class upper bounds on the number of independent parameters are explicitly given. The single input quadratic cost formulation contains exactly
n
independent parameters (functions).