Robust Control Under Uncertainty - A Review of Synthesis, Estimation, and Data-Driven Design

Robust control comprises design traditions that place the burden of uncertainty management in different parts of the closed loop. Minimax and structured synthesis allocate robustness offline; disturbance observers and related estimators seek nominal-performance recovery online; sliding and hybrid controllers pursue invariance or mode-dependent guarantees; stable inversion and output regulation address structural tracking feasibility; and predictive, distributed, safety-filtered, or data-driven methods incorporate constraints, information structure, and finite data. Because these paradigms certify different objects, nominal tracking error alone is an inadequate basis for comparison. This paper presents a critical narrative review of 170 foundational and recent sources spanning 1945–2026. The literature is evaluated through a common contract consisting of the uncertainty object, regulated property, mathematical certificate, and implementation envelope. The review connects sensitivity limitations, H-infinity and mu synthesis, LMIs and IQCs, decentralized and system-level synthesis, disturbance estimation, sliding-mode and switched control, stable inversion, robust and stochastic MPC, control-oriented identification, direct data-driven control, sampled-data implementation, delays, networks, saturation, and controller reduction. Particular attention is given to disagreements that are obscured by nominal comparisons: full-block versus structured uncertainty, fixed worst-case attenuation versus online recovery, deterministic versus probabilistic feasibility, direct versus indirect use of data, and nominal inversion versus robust regulation. The resulting guidance links method selection to uncertainty geometry, disturbance compensability, nonminimum-phase structure, actuator authority, communication, constraints, and data quality.