\( \mathcal{H}_\infty\) filtering for discrete-time nonlinear singular systems with quantization (Q1993336)

Summary: This paper investigates the problem of \(\mathcal{H}_{\infty}\) filtering for class discrete-time Lipschitz nonlinear singular systems with measurement quantization. Assume that the system measurement output is quantized by a static, memoryless, and logarithmic quantizer before it is transmitted to the filter, while the quantizer errors can be treated as sector-bound uncertainties. The attention of this paper is focused on the design of a nonlinear quantized \(\mathcal{H}_{\infty}\) filter to mitigate quantization effects and ensure that the filtering error system is admissible (asymptotically stable, regular, and causal), while having a unique solution with a prescribed \(\mathcal{H}_{\infty}\) noise attenuation level. By introducing some slack variables and using the Lyapunov stability theory, some sufficient conditions for the existence of the nonlinear quantized \(\mathcal{H}_{\infty}\) filter are expressed in terms of linear matrix inequalities (LMIs). Finally, a numerical example is presented to demonstrate the effectiveness of the proposed quantized filter design method.