Passivity Based Stability Condition for Interefered Digital Filters

Abstract

<em>This paper presents a new passivity condition for fixed-point state-space interfered digital filters using saturation arithmetic. Passivity is a way to characterize input-output stability of a system, that is, supplied bounded input energy produces bounded output energy. The presented criterion also ensures asymptotic stability of the state-space digital filter with zero external disturbances. The result is expressed in terms of linear matrix inequality, and therefore, can be solved via existing numerical packages. A numerical example is arranged to validate the usefulness of the proposed method.</em>

Analysis of Memory Effects in Digital Filters with Overflow Arithmetic

“…Using (10), (15) [16] focuses on saturation overflow arithmetic. By contrast, the present approach is applicable not only to saturation, but also to two's complement, zeroing, triangular overflow nonlinearities.…”

“…The problem of stability of digital filters with finite wordlength nonlinearities has been studied extensively [2][3][4][5][6][7][8][9][10][11][12][13][14]. Several stability results to reduce the effects of nonlinear phenomenon have appeared recently [10][11][12][13][14][15][16].…”

“…The analysis of undesired memory effects in digital filters with finite wordlength nonlinearities is an important problem. The criteria in [3][4][5][6][7][8][9][10][11][12][13][14][15] cannot be used to measure the memory effects in digital filters. Recently, the Hankel norm performance criterion for the reduction of memory effects of digital filters with saturation arithmetic has been established in [16].…”

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.…”

“…Hence, analysis of externally disturbed digital filters is one of the important research topics and has attracted continuous interest of researchers (Ahn, 2013a, 2013b; Ahn, 2014; Ahn and Shi 2016a, 2016b; Arockiaraj et al 2017; Kokil and Arockiaraj 2017; Kokil and Shinde 2017; Kokil et al, 2012, 2018; Kumar et al, 2019; Rani et al 2017). To address stability problems related to digital filters with disturbances, popular methods such as H ∞ filtering (Kokil et al, 2012, 2018), l 2 − l ∞ (Ahn, 2013a; Rani et al, 2017), induced l ∞ (Kokil and Arockiaraj, 2017; Kokil and Shinde, 2017), input-to-state stability (Ahn, 2014; Kumar et al, 2019) and passivity (Ahn, 2013b; Ahn and Shi, 2016a, 2016b; Arockiaraj et al, 2017) based approaches have been exploited. However, most of the existing results (Ahn, 2013a, 2013b, 2014; Ahn and Shi, 2016a, 2016b; Arockiaraj et al, 2017; Kokil and Arockiaraj, 2017; Kokil and Shinde, 2017; Kokil et al, 2012, 2018; Kumar et al, 2019; Rani et al, 2017<...>…”