Finite word length is a practical limitation when discrete-time systems are implemented by using digital hardware. This restriction degrades the performance of a discrete-time system and may even lead it toward instability. This paper, addresses the stability and disturbance attenuation performance analysis of nonlinear discrete-time systems under the influence of energy-bounded external interferences when such systems are subjected to quantization and overflow effects of fixed point hardware. The proposed methodology, in comparison with previous paper, describes exponential stability for the nonlinear discrete-time systems by considering composite nonlinearities of digital hardware. The proposed criteria that ensure exponential stability and [Formula: see text] performance index for the digital systems under consideration are presented in the form of a set of linear matrix inequalities (LMIs) by exploiting Lyapunov stability theory, Lipschitz condition and sector conditions for different types of commonly used quantization and overflow arithmetic properties, and the results are validated for recurrent neural networks. Furthermore, novel stability analysis results for a nonlinear discrete-time system under hardware constraints can also be observed as a special case of the proposed criteria.

中文翻译：

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存在量化和溢出约束的定点干扰非线性数字系统的指数稳定性分析

当使用数字硬件实现离散时间系统时，有限字长是一个实际限制。这种限制会降低离散时间系统的性能，甚至可能导致其不稳定。本文针对非线性离散时间系统在能量有界外部干扰影响下的稳定性和干扰衰减性能分析，该系统受到定点硬件的量化和溢出效应。与以前的论文相比，所提出的方法通过考虑数字硬件的复合非线性来描述非线性离散时间系统的指数稳定性。确保指数稳定性和[公式：见文本] 所考虑的数字系统的性能指标通过利用 Lyapunov 稳定性理论、Lipschitz 条件和不同类型常用量化和溢出算术属性的扇区条件，以一组线性矩阵不等式 (LMI) 的形式呈现，以及结果验证了循环神经网络。此外，硬件约束下非线性离散时间系统的新稳定性分析结果也可以作为所提出标准的特例来观察。