Improved stability results for uncertain discrete-time state-delayed systems in the presence of nonlinearities

Abstract

In this paper, delay-dependent linear matrix inequality (LMI)-based stability conditions have been developed for uncertain discrete-time state-delayed systems, in which nonlinear effects in the form of limit cycles may arise due to the finite word length implementation of such systems. Two problems have been addressed in this paper. The first problem considers the discrete-time system to be under the combined influence of quantization and overflow nonlinearities and in the second problem, the system is under the influence of saturation nonlinearities. The criteria developed are based on utilizing both the delay partitioning method and reciprocally convex approach. It is demonstrated with the help of numerical examples that the presented criteria are able to yield less conservative results along with lower computational complexity than previously reported criteria.

Finite-time boundedness for switched systems subject to both discrete and distributed delays

“…It is well known that time delays, as an inherent feature of many dynamics, exist widely in practical engineering systems and may cause instability or undesirable performance. For switched systems with time delay, there have already been some results (see Hua et al, 2014;Sun et al, 2006;Xie et al, 2008;Zhang and Yu, 2009, and references therein).Note that all the above results are concerned with discrete delays (Phat and Ratchagit, 2011;Phat et al, 2012;Rajchakit et al, 2013a,b;Song and He, 2014;Tadepalli and Kandanvli, 2014;Wang et al, 2013). In some cases, we should take into account distributed delay since the signal propagation may also be distributed during a certain period of time Zheng, 2007, Zuo et al, 2011).…”

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

“…Zeroing, triangular, saturation and two’s complement are the commonly used overflow characteristics in the digital filters (Claasen et al, 1976). Since saturation overflow arithmetic gives better stability region among the other overflow characteristics, it has been extensively studied (Ahn, 2013b; Ahn and Shi, 2016a, 2016b; Arockiaraj et al, 2017; Ji et al, 2011; Kandanvli and Kar, 2009; Kar and Singh, 2005; Kokil and Kar, 2012; Kokil et al, 2019; Kokil and Shinde, 2015; Parthipan et al, 2018; Parthipan and Kokil, 2020; Singh, 1985; Tadepalli and Kandanvli, 2016; Tadepalli et al, 2018). Therefore, stability analysis of digital filters using saturation arithmetic has become an important research problem.…”

Stability of Uncertain 2-D Discrete Systems in Presence of Generalized Overflow Nonlinearities

“…2-D models are needed as many times the one-dimensional (1-D) models are unable to capture the dynamics of the system. Such systems include image processing, monitoring and control of sensor networks, heat diffusion system (Xu & Yu, 2009), thermal processes (Tadepalli, Kandanvli, & Kar, 2015, 2016, iterative learning control (Tadepalli et al, 2015) etc. The 2-D modeling of physical systems has gained a lot of interest due to the two popular models Roesser (Roesser, 1975) and Fornasini Marchesini Second Local State-Space (FMSLSS) (Fornasini & Marchesini, 1978).…”