scholarly journals Stability Analysis of Drilling Inclination System with Time-Varying Delay via Free-Matrix-Based Lyapunov–Krasovskii Functional

2021 ◽  
Vol 25 (6) ◽  
pp. 1031-1038
Author(s):  
Zhen Cai ◽  
Guozhen Hu ◽  
◽  
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Stability Criterion ◽  
Coefficient Matrix ◽  
Positive Definite ◽  
Time Varying ◽  
Time Varying Delay ◽  
The Stability ◽  
Varying Delay ◽  
Insight Into

This study provides an insight into the asymptotic stability of a drilling inclination system with a time-varying delay. An appropriate Lyapunov–Krasovskii functional (LKF) is essential for the stability analysis of the abovementioned system. In general, an LKF is constructed with each coefficient matrix being positive definite, which results in considerable conservatism. Herein, to relax the conditions of the derived criteria, a novel LKF is proposed by avoiding the positive-definite restriction of some coefficient matrices and introducing additional free matrices simultaneously. Subsequently, this relaxed LKF is applied to derive a less conservative stability criterion for the abovementioned system. Finally, the effect of reducing the conservatism of the proposed LKF is verified based on two examples.

STABILITY CRITERION OF A CLASS OF NEUTRAL NEURAL NETWORK WITH UNCERTAINTIES AND TIME-VARYING DELAY

2011 ◽  
Vol 08 (01) ◽  
pp. 75-82
Author(s):  
JIANJUN TU ◽  
HANLIN HE
Keyword(s):  
Neural Network ◽  
Asymptotic Stability ◽  
Lyapunov Functional ◽  
Lyapunov Equation ◽  
Positive Definite ◽  
Time Varying ◽  
Time Varying Delay ◽  
Uniformly Asymptotic Stability ◽  
The Stability ◽  
Varying Delay

Under reasonable postulated conditions of time-varying delay, the stability of a class of neutral neural network is probed. Based on the proper construction of the Lyapunov functional, a new method of predicating the uniformly asymptotic stability of this kind of neutral network is presented. The criterion is based on the positive definite solutions of a Riccati equation and a discrete Lyapunov equation, and is converted to LMI problem. The validity of the criterion is also confirmed by the simulation.

A new control approach for a class of linear switched systems with time-varying delay

2021 ◽  
pp. 014233122199272
Author(s):  
Abbas Zabihi Zonouz ◽  
Mohammad Ali Badamchizadeh ◽  
Amir Rikhtehgar Ghiasi
Keyword(s):  
Stability Analysis ◽  
Linear Matrix Inequalities ◽  
Linear Matrix ◽  
Switching Systems ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
Linear Switching Systems ◽  
The Stability ◽  
Varying Delay

In this paper, a new method for designing controller for linear switching systems with varying delay is presented concerning the Hurwitz-Convex combination. For stability analysis the Lyapunov-Krasovskii function is used. The stability analysis results are given based on the linear matrix inequalities (LMIs), and it is possible to obtain upper delay bound that guarantees the stability of system by solving the linear matrix inequalities. Compared with the other methods, the proposed controller can be used to get a less conservative criterion and ensures the stability of linear switching systems with time-varying delay in which delay has way larger upper bound in comparison with the delay bounds that are considered in other methods. Numerical examples are given to demonstrate the effectiveness of proposed method.

scholarly journals Novel Robust Stability Criteria of Uncertain Systems with Interval Time-Varying Delay Based on Time-Delay Segmentation Method and Multiple Integrals Functional

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Xing He ◽  
Li-Jun Song ◽  
Yu-Bin Wu ◽  
Zi-Yu Zhou
Keyword(s):  
Stability Analysis ◽  
Robust Stability ◽  
Stability Criterion ◽  
Uncertain Systems ◽  
Previous Literature ◽  
Time Varying ◽  
Interval Time ◽  
Time Varying Delay ◽  
Varying Delay ◽  
Better Than

Interval time-varying delay is common in control process, e.g., automatic robot control system, and its stability analysis is of great significance to ensure the reliable control of industrial processes. In order to improve the conservation of the existing robust stability analysis method, this paper considers a class of linear systems with norm-bounded uncertainty and interval time-varying delay as the research object. Less conservative robust stability criterion is put forward based on augmented Lyapunov-Krasovskii (L-K) functional method and reciprocally convex combination. Firstly, the delay interval is partitioned into multiple equidistant subintervals, and a new Lyapunov-Krasovskii functional comprising quadruple-integral term is introduced for each subinterval. Secondly, a novel delay-dependent stability criterion in terms of linear matrix inequalities (LMIs) is given by less conservative Wirtinger-based integral inequality approach. Three numerical comparative examples are given to verify the superiority of the proposed approach in reducing the conservation of conclusion. For the first example about closed-loop control systems with interval time-varying delays, the proposed robust stability criterion could get MADB (Maximum Allowable Delay Bound) about 0.3 more than the best results in the previous literature; and, for two other uncertain systems with interval time-varying delays, the MADB results obtained by the proposed method are better than those in the previous literature by about 0.045 and 0.054, respectively. All the example results obtained in this paper clearly show that our approach is better than other existing methods.

scholarly journals Event-Triggered Stability Analysis of Semi-Markovian Jump Networked Control System with Actuator Faults and Time-Varying Delay via Bessel–Legendre Inequalities

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-16 ◽  
Author(s):  
Hongqian Lu ◽  
Chaoqun Guo ◽  
Yue Hu ◽  
Wuneng Zhou
Keyword(s):  
Control System ◽  
Stability Analysis ◽  
Networked Control System ◽  
Time Varying ◽  
Actuator Faults ◽  
Markovian Jump ◽  
Time Varying Delay ◽  
The Stability ◽  
Varying Delay ◽  
Event Triggered

This paper discusses the stability of semi-Markovian jump networked control system containing time-varying delay and actuator faults. The system dynamic is optimized while the network resource is saved by introducing an improved static event-triggered mechanism. For deriving a less conservative stability criterion, the Bessel–Legendre inequalities approach is employed to the stability analysis and plays a major role. By constructing the enhanced Lyapunov–Krasovskii functional (LKF) relevant to the Legendre polynomials, a stability criterion with lower conservativeness indexed by N is derived, and the conservativeness will decrease as N increases. In addition, a controller is designed. To prove the validity of this paper, numerical examples are provided at the last.

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