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

Time-variant systems represented by pairs of matrices and are said to be -equivalent if there exist differentiable matrices , and such that and -equivalent if . The extent of independent parameters (functions) in the quadratic cost formulation for a linear time-variant system is reported. For the -equivalent class and the - equivalent class upper bounds on the number of independent parameters are explicitly given. The single input quadratic cost formulation contains exactly independent parameters (functions).