Criterion for realizing state-delayed digital filters subjected to external interference employing saturation arithmetic

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

“…Therefore, many researchers have found interest in developing stability criteria for time-delay systems (Afshari et al, 2018; Liu et al, 2017c; Mobayen and Tchier, 2016; Pal and Negi, 2018). Several results have been reported in literature to address stability of discrete-time systems with state-delay and finite word length nonlinearities (Chen, 2009; Kandanvli and Kar, 2008, 2009, 2011, 2013; Kokil et al, 2019; Lee et al, 2012; Tadepalli et al, 2014, 2018; Xia et al, 2019).…”

“…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.…”

“…However, the techniques that appeared in Ahn (2011), Kokil et al (2012) and Li et al (2012) do not consider the effects of state-delay in the digital filters. Recently, a condition for state-delayed digital filters with external disturbance and saturation arithmetic to eliminate zero input limit-cycles has been established (Kokil et al, 2019). However, there is still a lot of scope remaining to improve the condition presented in Kokil et al (2019) to obtain better stability region.…”

“…Recently, a condition for state-delayed digital filters with external disturbance and saturation arithmetic to eliminate zero input limit-cycles has been established (Kokil et al, 2019). However, there is still a lot of scope remaining to improve the condition presented in Kokil et al (2019) to obtain better stability region.…”

“…If the stability region is larger, the flexibility of choosing filter coefficients would be better. Motivated by these concerns and inspired by the works of Ahn (2011), Kokil et al (2012, 2019) and Li et al (2012), the problem of exponential stability of externally interfered digital filters with state-delay and saturation arithmetic by ensuring H ∞ performance norm bound is addressed. With the help of Lyapunov-Krasovskii functional and improved saturations’ structural properties, a sufficient condition ensuring exponential stability is presented for the digital filters in the form of linear matrix inequality (LMI).…”