Delay-dependent stability and stabilisation of continuous 2D delayed systems with saturating control

Abstract

This paper deals with the stabilisation problem of continuous two-dimensional (2D) delayed systems, in the presence of saturations on the control signals. For this, a new delay decomposition approach is proposed to deal with the stability and stabilisation issues. The idea is that the range of variation of each delay is divided into segments, and a specific LyapunovKrasovskii functional is used that contains different weight matrices in each segment. Then, based on this approach, new delay-dependent stability and stabilisation criteria for continuous 2D delayed systems are derived. These criteria are less conservative and include some existing results as special cases. Some numerical examples are provided to show that a significant improvement is achieved using the proposed approach.

Stabilisation of continuous‐time switched 2D systems with all unstable modes

“…, and are real coefficient functions of , which is a switching signal and takes values in the set . By using similar processing method as [31] and defining we obtain the Roesser model of the form (10) with Note that in this case, and …”

Reliable H∞ control for 2‐D discrete switched systems with state delays and actuator failures

“…For 2‐D delayed systems, many improved approaches have been proposed in the literature, for instance, in Reference 21, some delay‐dependent stability criteria have been developed for 2‐D state‐delayed systems in the FM second model by using the free weighting matrices technique. By employing a delay decomposition approach in Reference 22, some delay‐dependent stability criteria for a class of continuous 2‐D systems with delays have been proposed. Recently, by the use of the auxiliary function‐based integral inequality, 20 the delay‐dependent stability problem for 2‐D continuous delayed systems has been studied in Reference 23.…”

Finite-time boundedness of two-dimensional positive continuous-discrete systems in Roesser model

“…H ∞ control or filtering of 2-D discrete systems were considered in Wu et al (2007, 2008). The corresponding results on 2-D continuous-time systems were also developed (see Badie et al, 2018; Emelianova et al, 2016; Hmamed et al, 2010, 2016, and references therein). Due to their special structures, the analysis of 2-D continuous-discrete systems becomes more difficult, and many scholars have been devoted themselves to the study of such systems in recently years.…”