Criterion for limit cycle-free state-space digital filters with external disturbances and generalized overflow non-linearities

Abstract

This paper investigates the problem of [Formula: see text] elimination of overflow oscillations in fixed-point state-space digital filters using generalized overflow non-linearities and external disturbance. The generalized overflow non-linearities under consideration cover the common types of overflow arithmetic used in practice, for instance zeroing, two’s complement, triangular and saturation. New criteria are established to ensure not only exponential stability, but also reduction in the effect of external disturbance to an [Formula: see text] norm constraint. The obtained criteria are in linear matrix inequality (LMI) framework and, hence, are computationally tractable. The presented approach constitutes a generalization over several previously reported approaches for the [Formula: see text] elimination of overflow oscillations. For saturation non-linearities, the presented result turns out to be less conservative than several existing criteria. Numerical examples are provided to demonstrate the effectiveness of the presented 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).…”

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

“…Existence of such nonlinearities causes instability to the designed system (Butterweck et al, 1988; Claasen et al, 1976; Oppenheim and Schafer, 1975; Schlichtharle, 2000). Therefore, several researchers have studied the stability properties of digital filters with saturation arithmetic (Ahn, 2011, 2013a, b; Bose and Chen, 1991; Kar, 2007, 2010; Kar and Singh, 1998, 2005; Kokil, 2016; Kokil and Shinde, 2015; Kokil et al, 2012a, 2012b, 2016; Liu and Michel, 1992; Singh, 1990).…”