An Improved Stability Criterion for Discrete-Time Linear Systems With Two Additive Time-Varying Delays

Abstract

In this paper, the stability analysis problem for discrete-time linear systems with additive time-varying delays is further investigated. In the first place, an augmented Lyapunov-Krasovskii functional (LKF) based on delay interval decomposition is designed, where some augmented vectors are selected to supplement the coupling relationships between some system state variables and different delay subintervals. In the second place, based on the augmented LKF, a new delay-dependent stability criterion is derived vai a general summation inequality lemma. The stability criterion is derived in the form of linear matrix inequality (LMI), which can be solved quickly by Matlab LMI-Tool. In the end, the effectiveness of the proposed method is illustrated by some common numerical examples.INDEX TERMS Discrete-time systems, Lyapunov-Krasovskii functional, Time-varying delays, Timedelayed system

Static anti-windup compensator design for locally Lipschitz systems under input and output delays

“…It is worth mentioning that the closed-loop system ( 4 ) is complicated to deal because of three delays, namely, input delay ι 1 ( t ), output delay ι 2 ( t ) and their combined effect ι 3 ( t ) (additive time-varying delay). All these three delays should be dealt in accordance with their properties, the later one, namely, additive time-delay for input output effect is most difficult as it contains the effects from both input and output delays [ 17 , 19 ]. The design should consider the individual constraints for time-delays ι 1 ( t ) and ι 2 ( t ) as well as the additive time-varying delay ι 3 ( t ).…”

“…Remark 4: In order to approximate the delay derivatives, several mathematical inequalities like Jensen's and Wirtinger have been used extensively in the literature [13][14][15][16][17][38][39][40]. Herein, state of the art methods like Wirtinger inequality, additive time-delay, and convex optimization algorithms are used to obtain inequality-based conditions for the AWC gain calculations.…”

“…In the recent decades, time-delay has become an active area of interest for the researchers due to its presence in several natural and physical systems like chemical processes, electrical circuits, power systems, control models, nuclear reactors, communication structures, and neural networks [15][16][17][18][19]. Time-delays have adverse effects on a system's performance and stability, as observed in [20].…”

“…Recently, static anti-windup scheme is proposed in [28] for the delayed nonlinear plants by employing reformulated Lipschitz condition and Wirtinger-based inequality; however, the results are applicable to a less general class of systems. Although, many aspects of time-delay systems have been addressed in the literature [15][16][17][18][19][20][21][22][23]; however, specifically, nonlinear timedelay systems with input saturation have not attained much research attention in the past decade. Therefore, further struggles are obligatory to explore new control and compensation schemes for nonlinear systems with input saturation and time-delay to address the aforementioned challenges.…”