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

Time-variant system represented by pairs of matrices (A(t), B(t)) and (A(t), B(t)) are said to be F-equivalent if there exist differentiable matrices C,G and D such that A = C-1 [(A+BG) - CC-1]C, B =C-1BD and K-equivalent if G ?? 0. The extent of independent parameters (functions) in the quadratic cost formulation for linear time-variant systems is reported in this paper. 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).