Implicit Euler discretization for chattering suppression in non-singular terminal sliding mode control

Numerical chattering limits digital implementation of non-singular terminal sliding mode control (NTSMC) despite its theoretical advantages. This paper presents an implicit Euler discretization for NTSMC that suppresses numerical chattering while preserving finite-time convergence through polynomial reformulation with signum-projection equivalence for explicit control computation. Discrete Lyapunov analysis establishes finite-time convergence and first-order accuracy, while strong numerical damping allows larger sampling periods than explicit methods. Comparative simulations with five discretization methods and hardware experiments on STM32-based PMSM control achieved 24-fold steady-state error reduction compared to explicit discretization and 0.083^∘ accuracy with 6.35 μs computation time at 2 kHz control.