New passivity results for the realization of interfered digital filters utilizing saturation overflow nonlinearities

Abstract

This paper considers the passivity performance analysis of fixed-point state-space digital filters with saturation nonlinearities in the presence of external interference. The purpose is to establish new stability criteria in terms of linear matrix inequality (LMI) such that fixed-point state-space digital filters with saturation nonlinearities in the existence of external interference ensure passivity performance with its storage function. The presented results not only ensure state strict and input state strict passivity in the presence of external interference but also confirm asymptotic stability without external interference. The obtained conditions for fixed-point state-space digital filters are based on passivity properties and, hence, are quite novel to previously proposed criteria. Finally, simulation results are given to demonstrate the effectiveness of the proposed work.

Hankel Norm Based Strict Passivity Performance of Digital Filter Using Saturation Nonlinearities

“…Due to this state in the system, there occurs external interference which results in instability and degrades the performance [8,9]. Thus, several results have been reported based on stability of digital filters with overflow nonlinearities when external disturbance is present [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24].…”

Stability of digital filters subject to external interference and state-delay

“…Zeroing, triangular, saturation and two’s complement are the commonly used overflow characteristics in the digital filters (Claasen et al, 1976). Since saturation overflow arithmetic gives better stability region among the other overflow characteristics, it has been extensively studied (Ahn, 2013b; Ahn and Shi, 2016a, 2016b; Arockiaraj et al, 2017; Ji et al, 2011; Kandanvli and Kar, 2009; Kar and Singh, 2005; Kokil and Kar, 2012; Kokil et al, 2019; Kokil and Shinde, 2015; Parthipan et al, 2018; Parthipan and Kokil, 2020; Singh, 1985; Tadepalli and Kandanvli, 2016; Tadepalli et al, 2018). Therefore, stability analysis of digital filters using saturation arithmetic has become an important research problem.…”

“…A generalized dissipativity criterion that includes l 2 − l ∞ and H ∞ performance indices in a unified framework has been presented (Ahn and Shi, 2016a). Further, very-strict (Arockiaraj et al, 2017) and state-strict (Parthipan et al, 2018) passivity criteria for externally disturbed digital filters using saturation arithmetic have been proposed. However, available passivity criteria (Ahn, 2013b; Ahn and Shi, 2016a, 2016b; Arockiaraj et al, 2017; Parthipan et al, 2018) are limited for the digital filters in the absence of state-delay.…”

“…Further, very-strict (Arockiaraj et al, 2017) and state-strict (Parthipan et al, 2018) passivity criteria for externally disturbed digital filters using saturation arithmetic have been proposed. However, available passivity criteria (Ahn, 2013b; Ahn and Shi, 2016a, 2016b; Arockiaraj et al, 2017; Parthipan et al, 2018) are limited for the digital filters in the absence of state-delay. So far, no result has been reported to provide a very-strict passivity criterion for interfered digital filters with state-delay and saturation arithmetic to the best of authors’ knowledge.…”

Overflow oscillations free implementation of state-delayed digital filter with saturation arithmetic and external disturbance

“…Saturation, two’s complement, triangular and zeroing are various forms of overflow nonlinearity correction techniques and on account of their catastrophic effects on the digital filters behavior, they have been addressed in literature (Arif et al, 2017; Butterweck et al, 1988; Kandanvli and Kar, 2008, 2009, 2013; Kar, 2007; Kar and Singh, 2004; Kokil and Arockiaraj, 2017; Kokil et al, 2018a, 2018b, 2018c, Kumar et al, 2019; Lee et al, 2012; Li et al, 2012, Singh, 2006). As it is evident from literature that the saturation overflow arithmetic produces the smallest deviation from the linear operation (Butterweck et al, 1988), the stability analysis of digital filters with saturation overflow has been considered as a forefront research problem (Ahn, 2011; Amjad et al, 2017; Arif et al, 2017; Kandanvli and Kar, 2009, 2013; Kar and Singh, 2004; Kokil and Arockiaraj, 2016; Kokil and Kar, 2012; Kokil and Shinde, 2015; Kokil et al, 2012; Lee et al, 2012; Parthipan et al, 2018; Singh, 1985; Tadepalli et al, 2014).…”