Overflow oscillation-free realization of digital filters with saturation

Abstract

Purpose The purpose of this paper is to establish a criterion for the global asymptotic stability of fixed-point state–space digital filters using saturation overflow arithmetic. Design/methodology/approach The method of stability analysis used in this paper is the second method of Lyapunov. The approach in this paper makes use of a precise upper bound of the state vector of the system and a novel passivity property associated with the saturation nonlinearities. Findings The presented criterion leads to an enhanced stability region in the parameter-space as compared to several existing criteria. Practical implications When dealing with the design of fixed-point state–space digital filters, it is desirable to have a criterion for selecting the filter coefficients so that the designed filter becomes free of overflow oscillations. The criterion presented in this paper provides enhanced saturation overflow stability region and therefore facilitates the designer greater flexibility in selecting filter parameters for overflow oscillation-free realization of digital filters. Originality/value The approach uses the structural properties of the saturation nonlinearities in a greater detail. The exploitation of upper bound of the system state vector together with a new passivity property of saturation nonlinearities is a unique feature of the present approach. The presented approach may lead to results not covered by several existing approaches.

Optimal guaranteed cost control of discrete-time uncertain systems subjected to state saturation nonlinearity

“…Jafari and Binazadeh (2020) and Zhu et al (2019) investigated the stability behavior of control systems with actuator saturation. The stability properties of DT systems with state saturation nonlinearities have been studied in Agarwal and Kar (2018), Alsaadi et al (2020), Kar (2010), Kar and Singh (2004), Kokil et al (2020), Shen et al (2020), and Singh (1985).…”

“…The existing approaches (Agarwal and Kar, 2018; Alsaadi et al, 2020; Kar, 2010; Kar and Singh, 2004; Kokil et al, 2020; Liu and Michel, 1992; Shen et al, 2020; Singh, 1985) deal with the global asymptotic stability problem of DT systems with state saturation. Therefore, such approaches are not suitable for realizing GC controllers.…”

New results for the realization of interfered direct-form digital filters with single two's complement nonlinearity

“…Various models of digital filter have been considered in the literature. Such models contain direct-form digital filters, including a single overflow nonlinearity (Singh, 2008(Singh, , 2010(Singh, , 2013Shen and Yuan, 2013), and state-space digital filters, including multiple saturation nonlinearities (Agarwal and Kar, 2018;Kar, 2010;Singh, 2012). Since the two's complement nonlinearity is a very strong nonlinearity, the stability conditions for the filter under consideration become the most restrictive.…”