scholarly journals Improved Results on Reachable Set Bounding for Linear Delayed Systems with Polytopic Uncertainties

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Hao Chen
Keyword(s):  
Reachable Set ◽  
Linear Matrix ◽  
Integral Functionals ◽  
Decomposition Technique ◽  
Matrix Inequalities ◽  
Functional Theory ◽  
Delayed Systems ◽  
Numerical Examples ◽  
Polytopic Uncertainties ◽  
Delay Decomposition

This paper focuses on bound of reachable sets for delayed linear systems with polytopic uncertainties. Based on Lyapunov-Krasovskii functional theory, delay decomposition technique, and reciprocally convex method, some new results expressed in the form of linear matrix inequalities are derived. It should be noted that triple integral functionals are first to be introduced for reachable set analysis. Consequently, a tighter bound of the reachable set is obtained. Four numerical examples are given to illustrate the effectiveness and advantage of the proposed results comparing with the existing criteria.

scholarly journals Passivity of Memristive BAM Neural Networks with Probabilistic and Mixed Time-Varying Delays

2018 ◽  
Vol 2018 ◽  
pp. 1-25
Author(s):  
Weiping Wang ◽  
Meiqi Wang ◽  
Xiong Luo ◽  
Lixiang Li ◽  
Wenbing Zhao
Keyword(s):  
Neural Networks ◽  
Probability Distribution ◽  
Linear Matrix ◽  
Time Varying ◽  
Bam Neural Networks ◽  
Bernoulli Distribution ◽  
Matrix Inequalities ◽  
Bidirectional Associative Memory ◽  
Leakage Delays ◽  
Numerical Examples

This paper is concerned with the passivity problem of memristive bidirectional associative memory neural networks (MBAMNNs) with probabilistic and mixed time-varying delays. By applying random variables with Bernoulli distribution, the information of probability time-varying delays is taken into account. Furthermore, we consider the probability distribution of the variation and the extent of the delays; therefore, the results derived are less conservative than in the existing papers. In particular, the leakage delays as well as distributed delays are all taken into consideration. Based on appropriate Lyapunov-Krasovskii functionals (LKFs) and some useful inequalities, several conditions for passive performance are established in linear matrix inequalities (LMIs). Finally, numerical examples are given to demonstrate the feasibility of the presented theories, and the results reveal that the probabilistic and mixed time-varying delays have an unstable influence on the system and should not be ignored.

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 Pinning Synchronization of Complex Dynamical Networks with Variable-Delayed Coupling by Periodically Intermittent Control

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Ranran Cheng ◽  
Xiaoyong Tian ◽  
Mingshu Peng ◽  
Jinchen Yu
Keyword(s):  
Theoretical Analysis ◽  
Lyapunov Functions ◽  
Linear Matrix ◽  
Intermittent Control ◽  
Variable Delay ◽  
Matrix Inequalities ◽  
Complete Synchronization ◽  
Numerical Examples ◽  
Periodically Intermittent Control ◽  
Scale Free

This paper studied the adaptive pinning synchronization in complex networks with variable-delay coupling via periodically intermittent control. Theoretical analysis is included by means of Lyapunov functions and linear matrix inequalities (LMI) to make all nodes reach complete synchronization. Moreover, the synchronization criteria do not impose any restriction on the size of time delay. Numerical examples including the regular, Watts–Strogatz and scale-free BA random topological architecture are provided to illustrate the importance of our theoretical analysis.

scholarly journals On Stability Analysis for Generalized Neural Networks with Time-Varying Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
M. J. Park ◽  
O. M. Kwon ◽  
E. J. Cha
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Asymptotic Stability ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Stability Criteria ◽  
Numerical Examples ◽  
Generalized Neural Networks

This paper deals with the problem of stability analysis for generalized neural networks with time-varying delays. With a suitable Lyapunov-Krasovskii functional (LKF) and Wirtinger-based integral inequality, sufficient conditions for guaranteeing the asymptotic stability of the concerned networks are derived in terms of linear matrix inequalities (LMIs). By applying the proposed methods to two numerical examples which have been utilized in many works for checking the conservatism of stability criteria, it is shown that the obtained results are significantly improved comparing with the previous ones published in other literature.

scholarly journals BIBO Stability Analysis for Delay Switched Systems with Nonlinear Perturbation

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Jincheng Wei ◽  
Peng Shi ◽  
Hamid Reza Karimi ◽  
Bo Wang
Keyword(s):  
Numerical Simulation ◽  
Switched Systems ◽  
Nonlinear Perturbation ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Functional Theory ◽  
Bibo Stability ◽  
Delay Dependent ◽  
Bounded Input

The problem of bounded-input bounded-output (BIBO) stability is investigated for a class of delay switched systems with mixed time-varying discrete and constant neutral delays and nonlinear perturbation. Based on the Lyapunov-Krasovskii functional theory, new BIBO stabilization criteria are established in terms of delay-dependent linear matrix inequalities. The numerical simulation is carried out to demonstrate the effectiveness of the results obtained in the paper.

Robust H∞ control of stochastic linear systems with input delay by predictor feedback

2017 ◽  
Vol 40 (7) ◽  
pp. 2396-2407
Author(s):  
Ali Javadi ◽  
Mohammad Reza Jahed-Motlagh ◽  
Ali Akbar Jalali
Keyword(s):  
Linear Systems ◽  
Multiplicative Noise ◽  
Sufficient Conditions ◽  
Input Delay ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
External Disturbances ◽  
Delayed Systems ◽  
Simulation Results ◽  
Stochastic Linear Systems

This study investigates the prediction-based (dynamic) stabilization of linear systems with input delay in the presence of external disturbances and multiplicative noise modelled as Itô type stochastic differential equations. Conventional memory-less (static) controllers are widely used for the stabilization of both deterministic and stochastic delayed systems. However, using these methods the upper bound for delay is strongly restricted. Motivated by acceptable performances of dynamic controllers for deterministic delayed systems, the extension of these methods for stochastic delayed systems is considered in this paper. The structure of the dynamic controller for stabilization of stochastic delayed systems is firstly derived utilizing the prediction vector. Then two sufficient conditions are given in the form of linear matrix inequalities that in the case of feasibility provide the stabilizing gain of the controller. Finally, simulation results are given to illustrate the effectiveness of the proposed method.

scholarly journals Less Conservative Control Design for Linear Systems with Polytopic Uncertainties via State-Derivative Feedback

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Emerson R. P. da Silva ◽  
Edvaldo Assunção ◽  
Marcelo C. M. Teixeira ◽  
Luiz Francisco S. Buzachero
Keyword(s):  
Linear Systems ◽  
Lyapunov Functions ◽  
State Feedback ◽  
Controller Design ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Polytopic Uncertainties ◽  
Parameter Dependent ◽  
Finsler’S Lemma ◽  
Time Linear

The motivation for the use of state-derivative feedback instead of conventional state feedback is due to its easy implementation in some mechanical applications, for example, in vibration control of mechanical systems, where accelerometers have been used to measure the system state. Using linear matrix inequalities (LMIs) and a parameter-dependent Lyapunov functions (PDLF) allowed by Finsler’s lemma, a less conservative approach to the controller design via state-derivative feedback, is proposed in this work, with and without decay rate restriction, for continuous-time linear systems subject to polytopic uncertainties. Finally, numerical examples illustrate the efficiency of the proposed method.

scholarly journals New relaxed stability and stabilization conditions for both discrete and differential linear repetitive processes

2021 ◽  
Author(s):  
Marcin Boski ◽  
Robert Maniarski ◽  
Wojciech Paszke ◽  
Eric Rogers
Keyword(s):  
Iterative Learning Control ◽  
Experimental Validation ◽  
Linear Matrix ◽  
Control Law ◽  
2D Systems ◽  
Matrix Inequalities ◽  
Repetitive Processes ◽  
Numerical Examples ◽  
Linear Repetitive Processes ◽  
Stability And Stabilization

AbstractThe paper develops new results on stability analysis and stabilization of linear repetitive processes. Repetitive processes are a distinct subclass of two-dimensional (2D) systems, whose origins are in the modeling for control of mining and metal rolling operations. The reported systems theory for them has been applied in other areas such iterative learning control, where, uniquely among 2D systems based designs, experimental validation results have been reported. This paper uses a version of the Kalman–Yakubovich–Popov Lemma to develop new less conservative conditions for stability in terms of linear matrix inequalities, with an extension to control law design. Differential and discrete dynamics are analysed in an unified manner, and supporting numerical examples are given.

scholarly journals H∞Control for Nonlinear Systems with Time-Varying Delay Using Matrix-Based Quadratic Convex Approach

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
C. Emharuethai ◽  
P. Niamsup
Keyword(s):  
Nonlinear System ◽  
State Feedback ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Numerical Examples ◽  
Time Varying Delay ◽  
Varying Delay

H∞control problem for nonlinear system with time-varying delay is considered by using a set of improved Lyapunov-Krasovskii functionals including some integral terms, and a matrix-based on quadratic convex, combined with Wirtinger's inequalities and some useful integral inequality.H∞controller is designed via memoryless state feedback control and new sufficient conditions for the existence of theH∞state feedback for the system are given in terms of linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the obtained result.

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