Cyclic Reformulation-Based Identification and Polytopic Uncertainty Modeling for Multirate Systems

Modern control systems increasingly rely on heterogeneous sensors operating at different sampling rates, where intermittently missing outputs pose fundamental challenges for system identification. This paper proposes a non-iterative, control-oriented identification method for multirate systems based on cyclic reformulation. The method transforms multirate data into an expanded time-invariant representation and yields M parameter sets from a single input-output dataset, where M is the least common multiple of the sensor sampling periods. These parameter sets, expressed in a common state coordinate of the original dimension, are used in two complementary ways: their centroid, in which each output row is averaged over the phases at which that output is observed, serves as a noise-reduced nominal model, while their convex hull gives a polytopic uncertainty model whose vertices can be used directly in vertex-based LMI robust control design. Building on the exact cyclic-structure recovery established in the authors' preceding work, the paper contributes the centroid and polytopic models and evaluates them under finite noise through output-level validation statistics. Numerical simulations support both models: an illustrative SISO example shows that the centroid attains higher validation FIT than the best individual vertex and substantially outperforms an interpolation-based baseline, while a MIMO multirate sensing example confirms that the constructed polytope contains models whose validation FIT exceeds 95% on average even at the highest tested noise level. The resulting polytope is a data-derived uncertainty description obtained from a single experiment, so that the framework links multirate system identification with robust-control-oriented uncertainty modeling without iterative EM-type optimization.