• Fellow of IEEE (The Institute of Electrical and Electronics Engineers), 1989
    Citation: "For contributions to filtering and estimation, stochastic control, and stochastic systems theory"

• Honorary Member of Hungarian Operational Research Society, 1994

• Elected Member of the Royal Swedish Academy of Engineering Sciences (IVA), 1996

• Elected Foreign Member of Russian Academy of Natural Sciences, 1997

• The paper A convex optimization approach to the rational covariance extension problem,by C. I. Byrnes,  S. V. Gusev and  A. Lindquist, published in SIAM J. Control and Opimization, 37 (1999), 211--229, has been chosen by the editors of SIAM Review to be a  "SIGEST paper",  the second paper ever from  SIAM Journal of Control and Optimization.