Two-wheeled self-balancing robots exhibit nonlinear and inherently unstable dynamics due to their inverted-pendulum structure, making control design challenging under terrain variations and external disturbances. This paper proposes a hybrid master–slave fuzzy cascade controller with an additional wheel-synchronization loop to improve tracking performance and robustness. The architecture combines a master velocity PI loop with fuzzy-tuned integral action and a slave balance PD loop with fuzzy proportional control, while a differential synchronization mechanism compensates for motor mismatches without affecting the global balance dynamics. Local stability is analyzed through linearization and equivalent gain approximation within a sector-bounded framework. Experimental validation was conducted on an ESP32-based TWSBR under flat, uphill, and downhill conditions at reference velocities of $0.15$, $0.20$, and $0.30{\displaystyle \frac{\mathrm{m}}{\mathrm{s}}}$, including payload tests with additional masses of $0.279$ and $0.375\mathrm{kg}$. For each scenario, 30 independent trials were performed to compute the reported metrics. Compared with a conventional PID controller, the proposed strategy reduced the flat-terrain velocity RMSE from $0.0108$ to $0.0057{\displaystyle \frac{\mathrm{m}}{\mathrm{s}}}$, while also improving angular stabilization and robustness under slope and payload disturbances.

Data-driven models for embedded control must account for acquisition filtering and experimental uncertainty while retaining dependence among identified parameters. This work develops a framework connecting identification in filtered-state coordinates, joint fuzzy uncertainty propagation, and fixed-gain stability assessment. A structured affine discrete-time model is refined through finite-horizon prediction error, and complete bootstrap deviations define a joint radial parameter family. Set inclusion ensures nested prediction envelopes, while endpoint quadratic inequalities certify stability over continuous parameter segments. Evaluation uses 30 identification runs and a main campaign of 60 physical closed-loop trials on a DC motor (30 per controller), complemented by two further campaigns of ten trials per controller: one with an inserted series resistor and one with a sinusoidal reference. Separate calibration and testing quantify predictive coverage and interval width, while marginal-preserving permutation demonstrates the influence of parameter pairing on prediction bands and sampled stability. All 435 retained training families receive continuous stability certificates. Quantitative comparisons with N4SID, SUBNET, and a TSK fuzzy predictor identify complementary predictive strengths, and nominal versus guaranteed-cost control evaluations characterize the trade-off between tracking accuracy and voltage effort. The implemented nominal integral LQR achieves a tracking RMSE of $0.7969\mathrm{rad}$. The contribution links empirical joint uncertainty to nested propagation and verifiable stability properties within the retained model families, supported by physical control experiments. The certificates apply to the modeled linear dynamics; experimental validation remains limited to the tested platform and operating conditions.