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.

scholarly journals Passivity analysis of multiple time-varying time delayed complex variable neural networks in finite-time

2021 ◽  
Vol 8 (4) ◽  
pp. 842-854
Author(s):  
N. Jayanthi ◽  
◽  
R. Santhakumari ◽  
Keyword(s):  
Neural Networks ◽  
Finite Time ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Linear Matrix ◽  
Multiple Time ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Complex Valued ◽  
Theoretical Results

In this article, we investigate the problem of finite-time passivity for the complex-valued neural networks (CVNNs) with multiple time-varying delays. To begin, many definitions relevant to the finite-time passivity of CVNNs are provided; then the suitable control inputs are designed to guarantee the class of CVNNs are finite-time passive. In the meantime, some sufficient conditions of linear matrix inequalities (LMIs) are derived by using inequalities techniques and Lyapunov stability theory. Finally, a numerical example is presented to illustrate the usefulness of the theoretical results.

scholarly journals Sufficient Conditions on the Exponential Stability of Neutral Stochastic Differential Equations with Time-Varying Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Yanwei Tian ◽  
Baofeng Chen
Keyword(s):  
Differential Equations ◽  
Exponential Stability ◽  
Stochastic Differential Equations ◽  
Lyapunov Stability ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Delay Dependent

The exponential stability is investigated for neutral stochastic differential equations with time-varying delays. Based on the Lyapunov stability theory and linear matrix inequalities (LMIs) technique, some delay-dependent criteria are established to guarantee the exponential stability in almost sure sense. Finally a numerical example is provided to illustrate the feasibility of the result.

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.

Exponential stability and periodicity of memristor-based recurrent neural networks with time-varying delays

2017 ◽  
Vol 10 (02) ◽  
pp. 1750027 ◽  
Author(s):  
Wei Zhang ◽  
Chuandong Li ◽  
Tingwen Huang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Functional Approach ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Matrix Inequalities ◽  
Inclusion Theory ◽  
The Stability

In this paper, the stability and periodicity of memristor-based neural networks with time-varying delays are studied. Based on linear matrix inequalities, differential inclusion theory and by constructing proper Lyapunov functional approach and using linear matrix inequality, some sufficient conditions are obtained for the global exponential stability and periodic solutions of memristor-based neural networks. Finally, two illustrative examples are given to demonstrate 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.

Global dissipativity of stochastic Lotka–Volterra system with feedback controls

2017 ◽  
Vol 10 (02) ◽  
pp. 1750022 ◽  
Author(s):  
Qimin Zhang ◽  
Xinjing Zhang ◽  
Hongfu Yang
Keyword(s):  
Linear Matrix Inequalities ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Jensen Inequality ◽  
Linear Matrix ◽  
Mean Square ◽  
Matrix Inequalities ◽  
Volterra System ◽  
Feedback Controls ◽  
The Mean

In this paper, a class of stochastic Lotka–Volterra system with feedback controls is considered. The purpose is to establish some criteria to ensure the system is globally dissipative in the mean square. By constructing suitable Lyapunov functions as well as combining with Jensen inequality and It[Formula: see text] formula, the sufficient conditions are established and they are expressed in terms of the feasibility to a couple linear matrix inequalities (LMIs). Finally, the main results are illustrated by examples.

Parameter-dependent robust H∞ filtering for uncertain two-dimensional discrete systems in the FM second model

2020 ◽  
Vol 37 (4) ◽  
pp. 1114-1132
Author(s):  
Khalid Badie ◽  
Mohammed Alfidi ◽  
Mohamed Oubaidi ◽  
Zakaria Chalh
Keyword(s):  
Asymptotic Stability ◽  
Lyapunov Function ◽  
Discrete Systems ◽  
Performance Criterion ◽  
Linear Matrix ◽  
Two Dimensional ◽  
Matrix Inequalities ◽  
Parameter Uncertainties ◽  
Error System ◽  
Parameter Dependent

Abstract This paper deals with the problem of robust $H_{\infty }$ filtering for uncertain two-dimensional discrete systems in the Fornasini–Marchesini second model with polytopic parameter uncertainties. Firstly, a new $H_{\infty }$ performance criterion is derived by exploiting a new structure of the parameter-dependent Lyapunov function. Secondly, based on the criterion obtained, a new condition for the existence of a robust $H_{\infty }$ filter that ensures asymptotic stability, and a prescribed $H_{\infty }$ performance level of the filtering error system, for all admissible uncertainties is established in terms of linear matrix inequalities. Finally, two examples are given to illustrate the effectiveness and advantage of the 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.

Mixed H2/H∞ Control for State-Delayed Linear Systems and a LMI Approach to the Solution of Coupled AREs

2003 ◽  
Vol 125 (2) ◽  
pp. 249-253 ◽  
Author(s):  
M. D. S. Aliyu
Keyword(s):  
Control Problem ◽  
Linear Systems ◽  
Linear Matrix Inequalities ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Riccati Equations ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Lmi Approach ◽  
Alternative Approach

In this paper, the state-feedback mixed H2/H∞ control problem for state-delayed linear systems is considered. Sufficient conditions for the solvability of this problem are given in terms of the solution to a pair of algebraic Riccati equations similar to the nondelayed case. However, these Riccati equations are more difficult to solve than those arising in the pure H2,H∞ problems, and an alternative approach is to solve a pair of linear matrix inequalities (LMIs).

scholarly journals An Improved Antiwindup Design Using an Anticipatory Loop and an Immediate Loop

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Qing Wang ◽  
Maopeng Ran ◽  
Chaoyang Dong ◽  
Maolin Ni
Keyword(s):  
Linear Matrix Inequalities ◽  
Continuous Time ◽  
Actuator Saturation ◽  
Sufficient Conditions ◽  
The Other ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Continuous Time Systems ◽  
Linear Invariant ◽  
Time Systems

We present an improved antiwindup design for linear invariant continuous-time systems with actuator saturation nonlinearities. In the improved approach, two antiwindup compensators are simultaneously designed: one activated immediately at the occurrence of actuator saturation and the other activated in anticipatory of actuator saturation. Both the static and dynamic antiwindup compensators are considered. Sufficient conditions for global stability and minimizing the inducedL2gain are established, in terms of linear matrix inequalities (LMIs). We also show that the feasibility of the improved antiwindup is similar to the traditional antiwindup. Benefits of the proposed approach over the traditional antiwindup and a recent innovative antiwindup are illustrated with well-known examples.

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