On the Stability Analysis of Equations with Bounded Time-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.

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

Journal of Advanced Computational Intelligence and Intelligent Informatics ◽

10.20965/jaciii.2021.p1031 ◽

2021 ◽

Vol 25 (6) ◽

pp. 1031-1038

Author(s):

Zhen Cai ◽

Guozhen Hu ◽

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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.

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

Complexity ◽

10.1155/2019/6927528 ◽

2019 ◽

Vol 2019 ◽

pp. 1-16 ◽

Cited By ~ 2

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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