• 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, was chosen by the editors of SIAM Review to be a SIGEST paper, the second paper ever from SIAM Journal of Control and Optimization
• George S. Axelby Outstanding Paper Award of the IEEE Control Systems Society (CSS) for the year 2003
• Zaborszky Lecturer for the year 2000