Passivity and Practical Stability of Fast-Sampled Quantized Discrete-Time Nonlinear Systems with Finite-Register Effects
Digital implementation of nonlinear control laws inevitably introduces quantization, saturation, and finite-word-length arithmetic that can degrade nominal stability. This paper develops an implementation-aware passivity framework for fast-sampled discrete-time nonlinear systems subject to quantized measurements, quantized actuation, and finite-register effects. All implementation nonlinearities are aggregated into a single structured input perturbation, which is propagated through the plant Lipschitz bound and a dissipation-type storage function. Three main results are established: (i) semi-passivity of the implemented closed loop is preserved provided the degraded dissipation function remains positive outside a compact set; (ii) practical stability with an explicit ultimate bound is guaranteed when disturbances are bounded; and (iii) for polynomial dissipation functions, global attraction to a prescribed residual ball is obtained. Design-oriented inequalities are derived that directly relate the admissible sampling period, quantization step sizes, and finite-register parameters to a guaranteed residual stability bound. Numerical validation on three examples a scalar nonlinear benchmark, a two-dimensional nonlinear system, and a digitally controlled DC-DC buck converter confirms that the proposed framework correctly predicts the monotone ordering of residual set sizes across all implementation scenarios, with analytical bounds conservative by less than 15 percent, and demonstrates that the derived design inequalities directly govern the achievable voltage regulation accuracy as a function of ADC word-length and sampling rate selection in embedded digital controller implementations.