Investigation of Memory Effects in Externally Interfered Nonlinear Digital Filter via Passivity Approach

This paper presents a new approach based on linear matrix inequalities to address the undesired memory effects in digitally filtered signals that are externally interfered with and subjected to quantization and overflow nonlinearities. The proposed method utilizes a passivity-based approach to effectively minimize the influence of previous external inputs on future outputs in the digital filters. The reduction of unwanted ringing can be assessed by evaluating the Hankel norm performance of the nonlinear digital filters. The proposed criteria ensure passive behavior based on the storage function and guarantee asymptotic stability when there is zero external input in the digital filters. Two numerical examples are provided to demonstrate the superiority of the proposed criterion.