An algorithm on constructing the diagonalizing matrix pair for H^∞-optimal control problem of the second kind

An algorithm is presented to obtain the diagonalizing matrix pair for the H^∞-optimal control problem of the second kind. This matrix pair can be calculated in time domain or in frequency domain approaches. The algorithm is recursive, since the original problems can be diagonalized layer by layer. This matrix pair is similar to the unitary matrix pair in singular-value decomposition with free parameter. They reflect some properties from given matrices such as the optimal norm for the diagonalizing matrix pair. This method can be applied to solve the superoptimal H^∞ control problem.