Delay partitioning approach to the robust stability of discrete-time systems with finite wordlength nonlinearities and time-varying delays

Abstract

This paper is associated with the problem of robust stability of discrete-time systems with time-varying delays and finite wordlength nonlinearities. The main contribution of the paper is two-fold. First, this paper presents a new Lyapunov function based on the idea of partitioning the delay interval into subintervals. The approach may be considered as an advancement over the several existing approaches where only the lower delay bound is partitioned. The second is that reciprocally convex inequality (RCI) and Wirtinger-based inequality (WBI) are used to estimate the sum terms involved in the forward difference of Lyapunov function. The intermediate delay is also included in the Lyapunov function to deal with the delay information more effectively. Finally, several examples are provided to illustrate the less conservatism of the proposed approach as compared to several existing results.

An anti-windup control strategy for discrete time-delay system based on triple Lyapunov functional

“…Time delay is a natural phenomenon which is inevitably present in all practical systems due to finite computation capability of real-time system and transportation lag in transmitted signals (Huang et al, 2022; Singh et al, 2021; Wang et al, 2020). It is a major cause of instability, poor performance, and oscillations (Chen et al, 2019; Kwon et al, 2013).…”

“…Furthermore, in this direction, new less-conservative stability results are derived by introducing different lemmas such as reciprocal convex inequality, Wirtinger inequality, triple Lyapunov–Krasovskii functional (LKF), bivariate quadratic function negative-determination lemma, and so on. (Kwon et al, 2013; Li et al, 2009; Liu and Zhang, 2012; Park et al, 2011; Singh et al, 2021; Sun et al, 2010). Nowadays, the use of microcontroller and fast, precise, and accurate digital processors has transformed the overall world into new domain of digitalization.…”

“…Nowadays, the use of microcontroller and fast, precise, and accurate digital processors has transformed the overall world into new domain of digitalization. Therefore, the research in the field of controller design related to discrete system is growing day by day (Chen et al, 2019; Singh et al, 2021).…”