Discrete implementations of sliding-mode controllers with barrier-function adaptations require a revised framework

This paper exposes a fundamental limitation in the discrete implementation of barrier-function-based adaptive sliding-mode controllers (BFASMCs). Under sampling, the predefined performance problem originally motivating these controllers becomes theoretically unsolvable, partly because of its infinite control authority. This contradicts the empirical success of BFASMCs in digital control, revealing a gap between theory and practice. We resolve this paradox by proposing a revised control framework that incorporates actuator saturation and sampled-data dynamics. Within this framework, we derive an explicit relation between actuator capacity, sampling rate, and barrier width, offering a principled tuning strategy. Finally, to validate the theoretical findings and the discussions given in the simulation section, an experimental study is performed on a ball-and-plate system.