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.

Fuzzy Control of a Class of Discrete-Time Fuzzy Bilinear Systems with Time-Delay

2012 ◽  
Vol 482-484 ◽  
pp. 1881-1885
Author(s):  
Jian Hu Jiang ◽  
Chao Wu ◽  
Yun Wang Ge ◽  
Li Jun Song
Keyword(s):  
Discrete Time ◽  
Sufficient Conditions ◽  
Bilinear System ◽  
Stability Control ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
The Stability ◽  
Varying Delay

The stability control problem is considered for a class of discrete-time T-S fuzzy bilinear system with time-varying delay in both state and input. Based on the parallel distribute compensation (PDC) scheme, some sufficient conditions are derived to guarantee the global asymptotically stability of the overall fuzzy system, which are represented in terms of matrix inequality. The corresponding controller can be obtained by solving a set of linear matrix inequalities. Finally, a simulation example shows that the approach is effective.

Robust Absolute Stability Criteria for Uncertain Lurie System With Interval Time-Varying Delay

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Pankaj Mukhija ◽  
Indra Narayan Kar ◽  
Rajendra K. P. Bhatt
Keyword(s):  
Absolute Stability ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Interval Time ◽  
Time Varying Delay ◽  
Wirtinger Inequality ◽  
Chua’S Oscillator ◽  
The Stability ◽  
Varying Delay

This paper addresses the problem of absolute stability of Lurie system with interval time-varying delay. The delay range is divided into two equal segments and an appropriate Lyapunov–Krasovskii functional (LKF) is defined. A tighter bounding technique for the derivative of LKF is developed. This bounding technique in combination with the Wirtinger inequality is used to develop the absolute stability criterion in terms of linear matrix inequalities (LMIs). The stability analysis is also extended to the Lurie system with norm-bounded parametric uncertainties. The effectiveness of the proposed approach has been illustrated through a numerical example and Chua's oscillator.

scholarly journals Improved Stability Criteria of Static Recurrent Neural Networks with a Time-Varying Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Lei Ding ◽  
Hong-Bing Zeng ◽  
Wei Wang ◽  
Fei Yu
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Improved Stability ◽  
The Stability ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

This paper investigates the stability of static recurrent neural networks (SRNNs) with a time-varying delay. Based on the complete delay-decomposing approach and quadratic separation framework, a novel Lyapunov-Krasovskii functional is constructed. By employing a reciprocally convex technique to consider the relationship between the time-varying delay and its varying interval, some improved delay-dependent stability conditions are presented in terms of linear matrix inequalities (LMIs). Finally, a numerical example is provided to show the merits and the effectiveness of the proposed methods.

scholarly journals Robust Stability of a Class of Uncertain Lur'e Systems of Neutral Type

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
W. Weera ◽  
P. Niamsup
Keyword(s):  
Neutral Type ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Lur’E Systems ◽  
Interval Time ◽  
Delay Function ◽  
Time Varying Delay ◽  
Bounded Nonlinearity ◽  
Varying Delay

This paper deals with the problem of stability for a class of Lur’e systems with interval time-varying delay and sector-bounded nonlinearity. The interval time-varying delay function is not assumed to be differentiable. We analyze the global exponential stability for uncertain neutral and Lur’e dynamical systems with some sector conditions. By constructing a set of improved Lyapunov-Krasovskii functional combined with Leibniz-Newton’s formula, we establish some stability criteria in terms of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness of the results.

Exponential Stability for Stochastic Neural Networks with Time-Varying Delay and Leakage Delay

2015 ◽  
Vol 742 ◽  
pp. 399-403
Author(s):  
Ya Jun Li ◽  
Jing Zhao Li
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Leakage Delay ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
Varying Delay

This paper investigates the exponential stability problem for a class of stochastic neural networks with leakage delay. By employing a suitable Lyapunov functional and stochastic stability theory technic, the sufficient conditions which make the stochastic neural networks system exponential mean square stable are proposed and proved. All results are expressed in terms of linear matrix inequalities (LMIs). Example and simulation are presented to show the effectiveness of the proposed method.

scholarly journals Stability Analysis for Uncertain Neural Networks of Neutral Type with Time-Varying Delay in the Leakage Term and Distributed Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Qi Zhou ◽  
Xueying Shao ◽  
Jin Zhu ◽  
Hamid Reza Karimi
Keyword(s):  
Neutral Type ◽  
Distributed Delay ◽  
Linear Matrix ◽  
Time Varying ◽  
Leakage Term ◽  
Time Varying Delay ◽  
The Stability ◽  
Uncertain Networks ◽  
Varying Delay ◽  
Stability Results

The stability problem is investigated for a class of uncertain networks of neutral type with leakage, time-varying discrete, and distributed delays. Both the parameter uncertainty and the generalized activation functions are considered in this paper. New stability results are achieved by constructing an appropriate Lyapunov-Krasovskii functional and employing the free weighting matrices and the linear matrix inequality (LMI) method. Some numerical examples are given to show the effectiveness and less conservatism of the proposed results.

scholarly journals Stability analysis for neural networks with discrete and leakage time-varying delay systems with delay-range-dependence and delay-derivative-dependence

2021 ◽  
Author(s):  
Pin-Lin Liu
Keyword(s):  
Neural Networks ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Decomposition Approach ◽  
Time Varying Delay ◽  
Systems Model ◽  
The Neural Networks ◽  
The Stability ◽  
Varying Delay

The paper deals with the stability problem of neural networks with discrete and leakage interval time-varying delays. Firstly, a novel Lyapunov-Krasovskii functional was constructed based on the neural networks leakage time-varying delay systems model. The delayed decomposition approach (DDA) and integral inequality techniques (IIA) were altogether employed, which can help to estimate the derivative of Lyapunov-Krasovskii functional and effectively extend the application area of the results. Secondly, by taking the lower and upper bounds of time-delays and their derivatives, a criterion on asymptotical was presented in terms of linear matrix inequality (LMI), which can be easily checked by resorting to LMI in Matlab Toolbox. Thirdly, the resulting criteria can be applied for the case when the delay derivative is lower and upper bounded, when the lower bound is unknown, and when no restrictions are cast upon the derivative characteristics. Finally, through numerical examples, the criteria will be compared with relative ones. The smaller delay upper bound was obtained by the criteria, which demonstrates that our stability criterion can reduce the conservatism more efficiently than those earlier ones.

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.

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.

Improved Results on Stability Criteria for Singular Systems with Interval Time-Varying Delays

2020 ◽  
pp. 2130001
Author(s):  
Chaibi Noreddine ◽  
Belamfedel Alaoui Sadek ◽  
Tissir El Houssaine ◽  
Bensalem Boukili
Keyword(s):  
Singular Systems ◽  
Singular System ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Small Gain ◽  
The Stability ◽  
Varying Delay ◽  
Singular Time

The purpose of this paper is to address the problem of assessing the stability of singular time-varying delay systems. In order to highlight the relations between the delay and the state, the singular system is transformed into a neutral form. Then, a model transformation using a three-terms approximation of the delayed state is exploited. Based on the lifting method and the Lyapunov–Krasovskii functional (LKF) method, a new linear matrix inequality (LMI) is obtained, allowing conclusions on stability to be drawn using the scaled small gain theorem (SSG). The use of SSG theorem for stability of singular systems with time-varying delay has not been investigated elsewhere in the literature. This represents the main novelty of this article. The result is applicable for assessing the stability of both singular systems and neutral systems with time-varying delays. The less conservativeness of the stability test is illustrated by comparison with recent literature results.

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