Segmentation of carotid intima-media (IM) borders from ultrasound sequences is challenging because of unknown image noise and varying IM border morphologies and/or dynamics. In this paper, we have developed a state-space framework to sequentially segment the carotid IM borders in each image throughout the cardiac cycle. In this framework, an ${\mathrm{H}}_{\mathrm{\infty }}$ filter is used to solve the state-space equations, and a grayscale-derivative constraint snake is used to provide accurate measurements for the ${\mathrm{H}}_{\mathrm{\infty }}$ filter. We have evaluated the performance of our approach by comparing our segmentation results to the manually traced contours of ultrasound image sequences of three synthetic models and 156 real subjects from four medical centers. The results show that our method has a small segmentation error (lumen intima, LI: 53 $\pm\, 67\;{\mathrm{\mu }}$m; media-adventitia, MA: 57 $\pm\, 63\;{\mathrm{\mu }}$m) for synthetic and real sequences of different image characteristics, and also agrees well with the manual segmentation (LI: bias = 1.44 ${\mathrm{\mu }}$m; MA: bias = $-$3.38 ${\mathrm{\mu }}$m). Our approach can robustly segment the carotid ultrasound sequences with various IM border morphologies, dynamics, and unknown image noise. These results indicate the potential of our framework to segment IM borders for clinical diagnosis.