scholarly journals Input and Output Passivity of Complex Dynamical Networks with General Topology

2010 ◽  
Vol 2010 ◽  
pp. 1-19
Author(s):  
Jinliang Wang
Keyword(s):  
Linear Matrix Inequalities ◽  
General Topology ◽  
Linear Matrix ◽  
Lyapunov Functionals ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Complex Dynamical Network ◽  
Dynamical Network ◽  
Input And Output ◽  
Generalized Complex

The input passivity and output passivity are investigated for a generalized complex dynamical network, in which the coupling may be nonlinear, time-varying, and nonsymmetric. By constructing some suitable Lyapunov functionals, some input and output passivity criteria are derived in form of linear matrix inequalities (LMIs) for complex dynamical network. Finally, a numerical example and its simulation are given to illustrate the efficiency of the derived results.

A novel method of topology identification for general complex dynamical networks with incomplete measurements

2018 ◽  
Vol 29 (05) ◽  
pp. 1840001
Author(s):  
Xinwei Wang ◽  
Guo-Ping Jiang ◽  
Xu Wu
Keyword(s):  
Linear Matrix Inequalities ◽  
Topological Structure ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Complex Dynamical Network ◽  
Topology Identification ◽  
Dynamical Network ◽  
General Complex ◽  
Novel Method ◽  
Mathematical Derivation

Recovering the topological structure of a general complex dynamical network with the incomplete measurements of transmitted drive states is investigated in this paper. The incomplete measurements, which cannot be ignored, have not been well considered in topology identification issue. Different from previous studies, we propose a novel method which can handle the situation of incomplete measurements well. The proposed method can fix the excessive deviation of the controller caused by the incomplete measurements, and overcome the special restrictions on the node dynamics raised by the previous methods. By means of LaSalle’s invariance principle, mathematical derivation of the mechanism is deduced rigorously to obtain the sufficient criteria in the form of linear matrix inequalities. Numerical simulations with the complex dynamical network composed of chaotic dynamical nodes are given to illustrate the effectiveness of our proposed method.

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 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.

scholarly journals Design and analysis of three nonlinearly activated ZNN models for solving time-varying linear matrix inequalities in finite time

2020 ◽  
Vol 390 ◽  
pp. 78-87 ◽  
Author(s):  
Yuejie Zeng ◽  
Lin Xiao ◽  
Kenli Li ◽  
Jichun Li ◽  
Keqin Li ◽  
...  
Keyword(s):  
Linear Matrix Inequalities ◽  
Finite Time ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities

Stability Analyses of Neural Networks with Unbounded Time-Varying Delays and Nonlinear Perturbations

2013 ◽  
Vol 278-280 ◽  
pp. 1247-1250 ◽  
Author(s):  
Li Zi Yin
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequalities ◽  
Functional Method ◽  
Neural Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Nonlinear Perturbations ◽  
Matrix Inequalities ◽  
Stability Analyses

In this paper, we consider the problem of mu-stability of unbounded time-varying delays neural systems with nonlinear perturbations. Some mu-stability criterias are derived by using Lyapunov- Krasovski functional method . Those criteria are expressed in the form of linear matrix inequalities (LMIs).

scholarly journals Distributed Event-Triggered Control of Multiagent Systems with Time-Varying Topology

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Jingwei Ma ◽  
Jie Zhou ◽  
Yanping Gao
Keyword(s):  
Multiagent Systems ◽  
Linear Matrix Inequalities ◽  
Linear Matrix ◽  
Control Input ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Common Lyapunov Function ◽  
Event Triggering ◽  
Lyapunov Function Method ◽  
Event Triggered

This paper studies the consensus of first-order discrete-time multiagent systems, where the interaction topology is time-varying. The event-triggered control is used to update the control input of each agent, and the event-triggering condition is designed based on the combination of the relative states of each agent to its neighbors. By applying the common Lyapunov function method, a sufficient condition for consensus, which is expressed as a group of linear matrix inequalities, is obtained and the feasibility of these linear matrix inequalities is further analyzed. Simulation examples are provided to explain the effectiveness of the theoretical results.

scholarly journals Robust Finite-TimeH∞Control for Linear Time-Varying Descriptor Systems with Jumps

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Xiaoming Su ◽  
Adiya Bao
Keyword(s):  
Linear Matrix Inequalities ◽  
Finite Time ◽  
Linear Time ◽  
Descriptor Systems ◽  
Feasibility Problem ◽  
Descriptor System ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Finite Time Boundedness

The finite-timeH∞control problem is addressed for uncertain time-varying descriptor system with finite jumps and time-varying norm-bounded disturbance. Firstly, a sufficient condition of finite-time boundedness for the abovementioned class of system is obtained. Then the result is extended to finite-timeH∞for the system. Based on the condition, state feedback controller is designed such that the closed-loop system is finite-time boundedness and satisfiesL2gain. The conditions are given in terms of differential linear matrix inequalities (DLMIs) and linear matrix inequalities (LMIs), and such conditions require the solution of a feasibility problem involving DLMIs and LMIs, which can be solved by using existing linear algorithms. Finally, a numerical example is given to illustrate the effectiveness of the method.

scholarly journals New Results on Passivity for Discrete-Time Stochastic Neural Networks with Time-Varying Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Wei Kang ◽  
Jun Cheng ◽  
Xiangyang Cheng
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequalities ◽  
Discrete Time ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Numerical Examples ◽  
Passivity Analysis ◽  
Delay Dependent

The problem of passivity analysis for discrete-time stochastic neural networks with time-varying delays is investigated in this paper. New delay-dependent passivity conditions are obtained in terms of linear matrix inequalities. Less conservative conditions are obtained by using integral inequalities to aid in the achievement of criteria ensuring the positiveness of the Lyapunov-Krasovskii functional. At last, numerical examples are given to show the effectiveness of the proposed method.

scholarly journals H∞ Control for LPV Discrete Systems with Random Time-Varying Network Delay

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Kewang Huang ◽  
Tao Ma ◽  
Feng Pan
Keyword(s):  
Linear Matrix Inequalities ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Discrete Systems ◽  
Performance Criterion ◽  
Random Time ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Network Delay

In this paper, we study the H∞ control problem for Linear Parameter Varying (LPV) discrete systems with random time-varying network delay. The state matrices of LPV discrete systems are deterministic functions and changed with parameters; the range of parameters is measurable. Considering the characteristics of networks with random time-varying delay, we proposed a new parameter-dependent H∞ performance criterion based on the Lyapunov stability theory. The coupling between Lyapunov functions and system matrices could be eliminated by introducing an additional matrix in this criterion, which made it easier for numerical implementation. On this basis, we designed a state feedback controller by virtue of linear matrix inequalities, which transformed the sufficient conditions into existence condition of solution of parametric linear matrix inequalities. The designed controller could keep the closed-loop system asymptotically stable under given time delay and probability and meet predefined performance metric. The validity of the proposed method is verified by numerical simulation.

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