From some basic relations in estimation theory, a comprehensive set of formulae are obtained for the periodic solution of Riccati equations. To obtain numerically stable algorithms, square root formulations are introduced. Both the discrete-time and continuous-time cases are considered. Closed-loop properties for periodic systems are also investigated. The results are applied to multirate measurement sampling. The control of a continuous stirred tank reactor serves as an illustrative example. The temperature measurements are then complemented by concentration analysis available at a slower rate than the basic sampling and control rate. The results give some guidelines about the benefits of multirate sampling.