Novel Results for Induced l∞ Stability for Digital Filters with External Noise

Abstract

This paper establishes novel criteria for the induced [Formula: see text] stability to avoid overflow oscillations in fixed-point digital filters with generalized overflow non-linearities and external noise. The proposed linear matrix inequality (LMI)-based criteria ensure exponential stability as well as confirm reduction in the influence of external noise. The generalized overflow non-linearities which are considered for analysis commonly occur in practice, viz. saturation, zeroing, two's complement, and triangular. The presented approach unifies a string of existing results which are derived by considering saturation non-linearities and external interference. Simulation examples are shown to validate the usefulness of the proposed approach.

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

“…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<...>…”

“…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) are not applicable to check stability of digital filters in the simultaneous presence of finite wordlength nonlinearities, external interference and state-delay.…”

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

“…In the realization of digital filters on finite wordlength machine, nonlinearities namely, quantization and overflow, are usually unavoidable (Ahn, 2011; Antoniou, 2006; Butterweck et al, 1988; Chen, 2009; Diksha et al, 2016; Kandanvli and Kar, 2008, 2009, 2011, 2013; Kar and Singh, 2004; Kokil and Arockiaraj, 2016, 2017; Kokil and Kar, 2012; Kokil and Shinde, 2015; Kokil et al, 2012, 2018a, 2018c; Li et al, 2012; Rehan et al, 2018; Schlichtharle, 2001; Singh, 1985; Tadepalli et al, 2014, 2018). The presence of these nonlinearities may lead digital filters to become as nonlinear systems.…”

“…The oscillations due to finite wordlength nonlinearities may cause performance degradation and instability of the designed system. 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).…”

“…The criteria reported in Chen (2009), Kandanvli and Kar (2008, 2013), Kar and Singh (2004), Kokil and Kar (2012), Lee et al (2012) and Singh (1985) are not sufficient enough to comment about the stability of digital filters in the presence of external interference. In order to deal with the effects of the external disturbance in the digital filters, several stability conditions have been presented (Ahn, 2011; Kokil and Arockiaraj, 2016, 2017; Kokil and Shinde, 2015; Kokil et al, 2012, 2018b, 2019; Kumar et al, 2019; Li et al, 2012). Therefore, stability analysis of the digital filters under simultaneous presence of saturation nonlinearities, state-delay and external disturbance is an important problem.…”