H ∞ Filtering for Discrete-Time Nonlinear Singular Systems with Quantization

Abstract EN

This paper investigates the problem of H∞ 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 H∞ 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 H∞ noise attenuation level.

By introducing some slack variables and using the Lyapunov stability theory, some sufficient conditions for the existence of the nonlinear quantized H∞ 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.