# $(J,J^0)$-dissipative matrices and singular $H_\infty$ control

Baramov, L. (1999) $(J,J^0)$-dissipative matrices and singular $H_\infty$ control. Proceedings of the 7th Mediterranean Conference on Control and Automation , 67-79.

This paper deals with solving a class of $H_\infty$ control problems where the transfer matrix from the external input to the measured output is invertible at infinity while there is no assumption about the infinite and/or imaginary-axis zeros of the transfer matrix from the control input to the penalized output. Our approach is based on the chain-scattering representation and a newly proposed $(J,J^0)$-dissipative factorization extending thus the well-known approach of H.~Kimura, while preserving its simplicity. We provide also a characterization of the set of controllers solving the given problem.