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

Abstract

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).