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

Abstract

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 are used in two complementary ways: their centroid serves as a noise-reduced nominal model, while their convex hull gives a polytopic uncertainty model compatible with vertex-based LMI robust control design. Building on the noise-free structural recovery theorem of the authors' preceding work, which is restated here in the notation of the present paper, the present paper newly introduces the centroid and polytopic models derived from the M parameter sets; finite-noise behavior is treated as an empirical observation and is evaluated numerically. 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, in line with the LTI counterpart, that the constructed polytope contains models whose validation FIT exceeds 95\% on average even at the highest tested noise level. The polytope is interpreted cautiously, with finite-noise behavior assessed through output-level validation statistics rather than realization-dependent matrix-coordinate distances. The proposed framework therefore links multirate system identification with robust-control-oriented uncertainty modeling without iterative EM-type optimization.