Strictly passive suppression of limit cycles in direct form digital filters with saturation nonlinearity: linear matrix inequality approach

Abstract

In this paper, we propose a new linear matrix inequality criterion for suppression of limit cycles in state–space direct form digital filters with saturation arithmetic and external interference via a passivity approach. The passive approach is employed to reduce the effect of external interference on the digital filter. The criterion guarantees not only asymptotic stability but also passivity from the external interference to the output vector. This criterion is in the form of linear matrix inequality; hence, it is computationally tractable. An example shows the effectiveness of the proposed criterion. Copyright © 2013 John Wiley & Sons, Ltd.

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<...>…”

“…However, passivity approach is not largely utilized to study stability of digital filters by considering finite wordlength nonlinearities. In Ahn (2013b), a passivity condition for externally disturbed digital filters with saturation arithmetic has been presented. New dissipativity criteria for direct form digital filters have been established (Ahn and Shi, 2016b).…”

“…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.…”

Condition of the elimination of overflow oscillations in two‐dimensional digital filters with external interference

“…Between these biquad filters, the mutual or external interferences always exist, and they usually bring negative effects, such as performance degradation or even destruction phenomenon. For this reason, Ahn has dealt with the research topic to the elimination of overflow oscillations (EOOs) for digital filters with external interference, such as EOOs [8], passive EOOs [9] and l 2 – l ∞ EOOs [10]. Here, it is very interesting to ask the first challenging question: ‘Is it possible to deal with EOOs, passive EOOs and l 2 – l ∞ EOOs of digital filters with external interference in a unified framework?’ On the other hand, two‐dimensional (2D) discrete systems have been studied widely in recent years because of their application in many areas such as thermal processes, water stream heating, image processing and so on [11–18].…”