A parameterization of parahermitian matrix functions and its application to a state-space solution for -analysis

In this paper, an economic parameterization for positive parahermitian matrix functions is introduced and applied to the μ -analysis framework wherein we propose a new state-space optimization problem for finding the required D -scales. Among the four state-space matrices to be used to realize the optimal D -scale, A and B are chosen via a Laguerre parameterization whereas the other two state-space matrices, C and D are obtained by spectral factorization after solving a convex optimization problem formulated in an LMI framework. The obtained D -scale satisfies the commuting property with the uncertainty structure. The proposed economic parameterization yields advantages in terms of less computational time and less number of decision variables and also, the proposed state-space optimization framework gives a frequency independent solution algorithm in state-space variables for the required D -scales. Two numerical examples are used to demonstrate the effectiveness of the proposed algorithm.