scholarly journals Stability andl1-Gain Analysis for Positive 2D Systems with State Delays in the Roesser Model

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Zhaoxia Duan ◽  
Hamid Reza Karimi ◽  
Zhengrong Xiang
Keyword(s):  
Sufficient Conditions ◽  
Linear Matrix ◽  
2D Systems ◽  
Matrix Inequalities ◽  
Roesser Model ◽  
State Delays ◽  
Lyapunov Function Method ◽  
2D System ◽  
Delay Dependent ◽  
Delay Dependent Stability

This paper considers the problem of delay-dependent stability andl1-gain analysis for positive 2D systems with state delays described by the Roesser model. Firstly, the copositive-type Lyapunov function method is used to establish the sufficient conditions for the addressed positive 2D system to be asymptotically stable. Then,l1-gain performance for the system is also analyzed. All the obtained results are formulated in the form of linear matrix inequalities (LMIs) which are computationally tractable. Finally, an illustrative example is given to verify the effectiveness of the proposed results.

scholarly journals A New Stability Criterion for Systems with Distributed Time-Varying Delays via Mixed Inequalities Method

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Jun-kang Tian ◽  
Yan-min Liu
Keyword(s):  
Linear Matrix Inequalities ◽  
Stability Criterion ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Numerical Examples ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
New Inequalities

This paper is concerned with the delay-dependent stability of systems with distributed time-varying delays. The novelty relies on the use of some new inequalities which are less conservative than some existing inequalities. A less conservative stability criterion is obtained by constructing some new augmented Lyapunov–Krasovskii functionals, which are given in terms of linear matrix inequalities. The effectiveness of the presented criterion is demonstrated by two numerical examples.

Stability of nonlinear time-delay systems satisfying a quadratic constraint

2016 ◽  
Vol 40 (3) ◽  
pp. 712-718 ◽  
Author(s):  
Mohsen Ekramian ◽  
Mohammad Ataei ◽  
Soroush Talebi
Keyword(s):  
Time Delay ◽  
Uncertain Systems ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Matrix Inequalities ◽  
Quadratic Constraint ◽  
The Stability ◽  
Delay Dependent ◽  
Delay Dependent Stability

The stability problem of nonlinear time-delay systems is addressed. A quadratic constraint is employed to exploit the structure of nonlinearity in dynamical systems via a set of multiplier matrices. This yields less conservative results concerning stability analysis. By employing a Wirtinger-based inequality, a delay-dependent stability criterion is derived in terms of linear matrix inequalities for the nominal and uncertain systems. A numerical example is used to demonstrate the effectiveness of the proposed stability conditions in dealing with some larger class of nonlinearities.

scholarly journals Novel Stability Analysis for Uncertain Neutral-Type Lur’e Systems with Time-Varying Delays Using New Inequality

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Yanmeng Wang ◽  
Lianglin Xiong ◽  
Yongkun Li ◽  
Haiyang Zhang ◽  
Chen Peng
Keyword(s):  
Stability Analysis ◽  
Neutral Type ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Lur’E Systems ◽  
New Class ◽  
Inequality Techniques ◽  
Delay Dependent ◽  
Delay Dependent Stability

This paper considers the delay-dependent stability analysis of neutral-type Lur’e systems with time-varying delays and sector bounded nonlinearities. First of all, using constructed function methods, a new Jensen-like inequality is introduced to obtain less conservative results. Second, a new class of Lyapunov-Krasovskii functional (LKF) is constructed according to the characteristic of the considered systems. Third, combining with the new inequality and reciprocal convex approach and some other inequality techniques, the new less conservative robust stability criteria are shown in the form of linear matrix inequalities (LMIs). Finally, three examples demonstrate the feasibility and the superiority of our methods.

scholarly journals Delay-Dependent Stability Analysis for Recurrent Neural Networks with Time-Varying Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Shu Lv ◽  
Junkang Tian ◽  
Shouming Zhong
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Stability Criteria ◽  
Activation Functions ◽  
New Class ◽  
Delay Dependent ◽  
Delay Dependent Stability

This paper concerns the problem of delay-dependent stability criteria for recurrent neural networks with time varying delays. By taking more information of states and activation functions as augmented vectors, a new class of the Lyapunov functional is proposed. Then, some less conservative stability criteria are obtained in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are given to illustrate the effectiveness of the proposed method.

scholarly journals BIBO Stabilization of Discrete-Time Stochastic Control Systems with Mixed Delays and Nonlinear Perturbations

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Xia Zhou ◽  
Yong Ren ◽  
Shouming Zhong
Keyword(s):  
Control Systems ◽  
Stochastic Control ◽  
Discrete Time ◽  
Linear Matrix ◽  
Mixed Delays ◽  
Nonlinear Perturbations ◽  
Matrix Inequalities ◽  
Delay Dependent ◽  
Bounded Input ◽  
Delay Dependent Stability

The problem of bounded-input bounded-output (BIBO) stabilization in mean square for a class of discrete-time stochastic control systems with mixed time-varying delays and nonlinear perturbations is investigated. Some novel delay-dependent stability conditions for the previously mentioned system are established by constructing a novel Lyapunov-Krasovskii function. These conditions are expressed in the forms of linear matrix inequalities (LMIs), whose feasibility can be easily checked by using MATLAB LMI Toolbox. Finally, a numerical example is given to illustrate the validity of the obtained results.

scholarly journals Absolute Stability of a Class of Nonlinear Singular Systems with Time Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Hong-Bing Zeng ◽  
Gang Chen ◽  
Shen-Ping Xiao
Keyword(s):  
Time Delay ◽  
Absolute Stability ◽  
Singular Systems ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Lmi Optimization ◽  
Nonlinear Singular Systems ◽  
Resulting Condition ◽  
Delay Dependent ◽  
Delay Dependent Stability

This paper deals with the absolute stability for a class of nonlinear singular systems with time delay. By employing a new Lyapunov-Krasovskii functional with the idea of partitioning delay length, improved delay-dependent stability criteria are established. The resulting condition is formulated in terms of linear matrix inequalities (LMIs), which is easy to be verified by exiting LMI optimization algorithms. A numerical example is given to show the effectiveness of the proposed technique and its improvements over the existing results.

New Delay-Dependent Stability Criteria for Recurrent Neural Networks with Time-Varying Delays

2014 ◽  
Vol 513-517 ◽  
pp. 922-926
Author(s):  
Ze Rong Ren ◽  
Xiang Jun Xie
Keyword(s):  
Neural Networks ◽  
Stability Criterion ◽  
Recurrent Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Neuron Activation ◽  
Delay Dependent ◽  
Delay Partitioning ◽  
Delay Dependent Stability

This paper is concerned with the problem of delay-dependent asymptotic stability criterion for recurrent neural networks with time-varying delays. A new Lyapunov functional is introduced by considering the information of neuron activation functions adequately. By using the improved delay-partitioning method and reciprocally convex approach, a less conservative stability criterion is obtained in terms of linear matrix inequalities (LMIs). A numerical example is finally given to illustrate the effectiveness of the derived method.

New Delay Dependent Stability Analysis for Switched Neutral Systems with Mode-Dependent Delays under Arbitrary Switching Laws

2011 ◽  
Vol 228-229 ◽  
pp. 993-1000
Author(s):  
Liang Lin Xiong ◽  
Xin Wang ◽  
Zhu Yuan Yang
Keyword(s):  
Stability Analysis ◽  
Lyapunov Functional ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Neutral Systems ◽  
Arbitrary Switching ◽  
The Stability ◽  
Switched Neutral Systems ◽  
Delay Dependent ◽  
Delay Dependent Stability

In this paper, the stability analysis of switched uncertain neutral systems with mode-dependent delays under arbitrary switching rules is presented. Based on common Lyapunov functional, and combined with the analysis of matrix inequalities, the delay dependent stability conditions are obtained in the form of linear matrix inequalities(LMIs)which can be easily solved by LMI toolbox in Matlab. Finally, a numerical example illustrate that the proposed criteria are effective.

New Approach to Delay-Dependent Control for Fuzzy Time-Delay Systems

2012 ◽  
Vol 482-484 ◽  
pp. 291-299
Author(s):  
Gang Guo
Keyword(s):  
Time Delay ◽  
Fuzzy Systems ◽  
Control Method ◽  
Delay Systems ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
New Approach ◽  
Stabilization Condition ◽  
Delay Dependent ◽  
Delay Dependent Stability

A new control method is proposed for stability analysis and stabilization problems for T-S fuzzy systems with time-delay. A new fuzzy Lyapunov-Krasovskii functional is introduced to establish some delay-dependent stability criteria. Based on parallel distributed compensation (PDC) scheme, a delay-dependent stabilization condition is derived and the corresponding controller can be obtained by solving a set of linear matrix inequalities (LMIs). Finally, simulation examples show that the effectiveness and benefits of the proposed method.

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