Department of Applied Mathematics & Physics, Kyoto University

Technical Report 2000-001 (March 31, 2000)

A Non-Standard J-Spectral Factorization of Rational Matrices via Generalized Algebraic Riccati Equation
by Atsushi Kawamoto and Tohru Katayama

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This paper considers a non-standard J-spectral factorization (NS-J-SFP) of a rational spectral matrix, which is related to the non-standard H_\infty control problem for a descriptor system. We derive necessary and sufficient conditions for the existence of a semi-stabilizing solution of a generalized algebraic Riccati equation (GARE). We then develop the solvability condition for the NS-J-SFP by adapting the zero compensation technique of Copeland and Safonov [7] and Xin and Kimura [26] to the descriptor system. Thus we can conclude that the NS-J-SFP is solvable if and only if the GARE has a semi-stabilizing solution. A numerical result is also included.