An L-lossless factorization approach to the positive real control problem

In this paper, we consider the generalized plant used in H∞ control problem and formulate the problem of making the closed-loop transfer function matrices positive real by output feedback. At first, this problem is solved in frequency domain by using the concept of the lossless positive real and the conjugation, and is reduced to finding an L-lossless factorization of a certain matrix as well as a well-known J-lossless factorization. An L-lossless system in this paper is the representation as a chain-scattering matrix of a lossless positive real system. Next, we expand this theory to the time domain by the generalized L-lossless factorization and the chain-scattering representation of the plant. As the result, this problem is reduced to solving the 2-Riccati equations like the H∞ control problem.