scholarly journals Finite-Time Passivity and Passification Design for Markovian Jumping Systems with Mode-Dependent Time-Varying Delays

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Chao Ma
Keyword(s):  
Finite Time ◽  
Functional Method ◽  
Linear Matrix ◽  
Time Varying ◽  
Markovian Jumping ◽  
Markovian Jumping Systems ◽  
The Mean ◽  
Delay Dependent ◽  
Passivity And Passification ◽  
Theoretical Results

This paper investigates the finite-time passivity and passification design problem for a class of Markovian jumping systems with mode-dependent time-varying delays. By employing the Lyapunov-Krasovskii functional method, delay-dependent sufficient criteria are derived to ensure the mean-square stochastically finite-time passivity. Based on the established results, mode-dependent passification controller is further designed in terms of linear matrix inequalities, such that the prescribed passive performance index of the resulting closed-loop system can be satisfied. Finally, two illustrative examples are given to show the effectiveness of the obtained theoretical results.

scholarly journals Passivity Analysis and Passive Control for T-S Fuzzy Systems with Leakage Delay and Mixed Time-Varying Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Ting Lei ◽  
Zengshun Chen ◽  
Qiankun Song ◽  
Zhenjiang Zhao
Keyword(s):  
Fuzzy Systems ◽  
Passive Control ◽  
Functional Method ◽  
Leakage Delay ◽  
Linear Matrix ◽  
Time Varying ◽  
The Matrix ◽  
Delay Dependent ◽  
Takagi Sugeno ◽  
Passivity And Passification

The passivity and passification for Takagi-Sugeno (T-S) fuzzy systems with leakage delay and both discrete and distributed time-varying delays are investigated. By employing the Lyapunov functional method and using the matrix inequality techniques, several delay-dependent criteria to ensure the passivity and passification of the considered T-S fuzzy systems are established in terms of linear matrix inequalities (LMIs) that can be easily checked by using the standard numerical software. The obtained results generalize some previous results. Two examples are given to show the effectiveness of the proposed criteria.

scholarly journals Resilient Robust Finite-TimeL2-L∞Controller Design for Uncertain Neutral System with Mixed Time-Varying Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Xia Chen ◽  
Shuping He
Keyword(s):  
Finite Time ◽  
State Feedback ◽  
Controller Design ◽  
Linear Matrix ◽  
Neutral System ◽  
Time Varying ◽  
Constraint Condition ◽  
Closed Loop System ◽  
Delayed System ◽  
Delay Dependent

The delay-dependent resilient robust finite-timeL2-L∞control problem of uncertain neutral time-delayed system is studied. The disturbance input is assumed to be energy bounded and the time delays are time-varying. Based on the Lyapunov function approach and linear matrix inequalities (LMIs) techniques, a state feedback controller is designed to guarantee that the resulted closed-loop system is finite-time bounded for all uncertainties and to satisfy a givenL2-L∞constraint condition. Simulation results illustrate the validity of the proposed approach.

Stabilization of Fuzzy Markovian Jumping Systems with Distributed Delay

2014 ◽  
Vol 556-562 ◽  
pp. 4386-4390
Author(s):  
Zhao Ping Yuan
Keyword(s):  
Time Delay ◽  
Robust Stabilization ◽  
Distributed Delay ◽  
Lyapunov Stability Theory ◽  
Linear Matrix ◽  
Markovian Jumping ◽  
Weighting Matrix ◽  
Markovian Jumping Systems ◽  
Distributed Time Delay ◽  
Delay Dependent

This paper is concerned with the stabilization problem for fuzzy Markovian jumping systems with distributed time delay. First, fuzzy Markovian jumping systems with distributed time delay are peoposed. Second, a novel criterion of delay-dependent robust stabilization for fuzzy Markovian jumping systems is established in terms of linear matrix inequalities (LMIs) by using Lyapunov stability theory and free-weighting matrix method. When these LMIS are feasible, an explicit expression of a desired adjustable state feedback controller is given. Based on the obtained criterion, the introduced controller ensures the overall closed-loop system asymptotically stable in mean square sense for all admissible uncertainties and time delay.

On Improved Delay-Range-Dependent Stability Criteria for Linear Systems with Interval Time-Varying Delay

2013 ◽  
Vol 427-429 ◽  
pp. 1306-1310
Author(s):  
Jun Jun Hui ◽  
He Xin Zhang ◽  
Fei Meng ◽  
Xin Zhou
Keyword(s):  
Functional Method ◽  
Linear Matrix ◽  
Time Varying ◽  
Stability Criteria ◽  
Interval Time ◽  
Time Varying Delay ◽  
Weighting Matrix ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

In this paper, we consider the problem of robust delay-dependent stability for a class of linear uncertain systems with interval time-varying delay. By using the directly Lyapunov-Krasovskii (L-K) functional method, integral inequality approach and the free weighting matrix technique, new less conservative stability criteria for the system is formulated in terms of linear matrix inequalities .Numerical examples are given to show the effectiveness of the proposed approach.

scholarly journals Stability of impulsive Hopfield neural networks with Markovian switching and time-varying delays

2011 ◽  
Vol 21 (1) ◽  
pp. 127-135 ◽  
Author(s):  
Ramachandran Raja ◽  
Rathinasamy Sakthivel ◽  
Selvaraj Anthoni ◽  
Hyunsoo Kim
Keyword(s):  
Neural Networks ◽  
Hopfield Neural Networks ◽  
Markovian Switching ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Stability Criteria ◽  
Markovian Jumping ◽  
Discrete State ◽  
Delay Dependent

Stability of impulsive Hopfield neural networks with Markovian switching and time-varying delaysThe paper is concerned with stability analysis for a class of impulsive Hopfield neural networks with Markovian jumping parameters and time-varying delays. The jumping parameters considered here are generated from a continuous-time discrete-state homogenous Markov process. By employing a Lyapunov functional approach, new delay-dependent stochastic stability criteria are obtained in terms of linear matrix inequalities (LMIs). The proposed criteria can be easily checked by using some standard numerical packages such as the Matlab LMI Toolbox. A numerical example is provided to show that the proposed results significantly improve the allowable upper bounds of delays over some results existing in the literature.

scholarly journals Finite-Time H ∞ State Estimation for Markovian Jump Neural Networks with Time-Varying Delays via an Extended Wirtinger’s Integral Inequality

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Saravanan Shanmugam ◽  
M. Syed Ali ◽  
R. Vadivel ◽  
Gyu M. Lee
Keyword(s):  
Neural Networks ◽  
Finite Time ◽  
Transition Probabilities ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Markovian Jump ◽  
Markovian Jumping ◽  
Double Inequality ◽  
Markovian Jump Neural Networks

This study investigates the finite-time boundedness for Markovian jump neural networks (MJNNs) with time-varying delays. An MJNN consists of a limited number of jumping modes wherein it can jump starting with one mode then onto the next by following a Markovian process with known transition probabilities. By constructing new Lyapunov–Krasovskii functional (LKF) candidates, extended Wirtinger’s, and Wirtinger’s double inequality with multiple integral terms and using activation function conditions, several sufficient conditions for Markovian jumping neural networks are derived. Furthermore, delay-dependent adequate conditions on guaranteeing the closed-loop system which are stochastically finite-time bounded (SFTB) with the prescribed H ∞ performance level are proposed. Linear matrix inequalities are utilized to obtain analysis results. The purpose is to obtain less conservative conditions on finite-time H ∞ performance for Markovian jump neural networks with time-varying delay. Eventually, simulation examples are provided to illustrate the validity of the addressed method.

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 A New Approach for Exponential Stability Criteria of New Certain Nonlinear Neutral Differential Equations with Mixed Time-Varying Delays

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 737
Author(s):  
Janejira Tranthi ◽  
Thongchai Botmart ◽  
Wajaree Weera ◽  
Piyapong Niamsup
Keyword(s):  
Exponential Stability ◽  
Model Transformation ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
New Approach ◽  
Neutral Differential Equations ◽  
Leibniz Formula ◽  
Delay Dependent ◽  
Theoretical Results

This work is concerned with the delay-dependent criteria for exponential stability analysis of neutral differential equation with a more generally interval-distributed and discrete time-varying delays. By using a novel Lyapunov–Krasovkii functional, descriptor model transformation, utilization of the Newton–Leibniz formula, and the zero equation, the criteria for exponential stability are in the form of linear matrix inequalities (LMIs). Finally, we present the effectiveness of the theoretical results in numerical examples to show less conservative conditions than the others in the literature.

Reliable mode-dependent memorized projective lag synchronization for semi-Markovian jumping coupled networks

2021 ◽  
pp. 095965182199136
Author(s):  
Yidao Ji ◽  
Wei Wu
Keyword(s):  
Mean Square ◽  
Lag Synchronization ◽  
Markovian Jumping ◽  
Synchronization Problem ◽  
Coupled Networks ◽  
Projective Lag Synchronization ◽  
The Mean ◽  
Delay Dependent ◽  
Synchronization Scheme ◽  
Theoretical Results

This article investigates the reliable projective lag synchronization problem for semi-Markovian jumping coupled networks under the master–slave framework. More precisely, a novel mode-dependent memorized synchronization scheme is proposed for the master and slave dynamical networks. By utilizing the Lyapunov-Krasovskii method, sufficient delay-dependent conditions are derived to achieve the reliable synchronization in the mean-square sense. Based on the derived results, the mode-dependent synchronization controller is further designed by convex optimization. In the end, two numerical examples are given to illustrate the effectiveness of the obtained theoretical results.

scholarly journals Passivity Analysis of Markovian Jumping Neural Networks with Leakage Time-Varying Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-17 ◽  
Author(s):  
N. Mala ◽  
A. R. Sudamani Ramaswamy
Keyword(s):  
Neural Networks ◽  
Upper Bound ◽  
Leakage Delay ◽  
Linear Matrix ◽  
Mixed Delays ◽  
Time Varying ◽  
Markovian Jumping ◽  
Mixed Time Delays ◽  
Passivity Analysis ◽  
Delay Dependent

This paper is concerned with the passivity analysis of Markovian jumping neural networks with leakage time-varying delays. Based on a Lyapunov functional that accounts for the mixed time delays, a leakage delay-dependent passivity conditions are derived in terms of linear matrix inequalities (LMIs). The mixed delays includes leakage time-varying delays, discrete time-varying delays, and distributed time-varying delays. By employing a novel Lyapunov-Krasovskii functional having triple-integral terms, new passivity leakage delay-dependent criteria are established to guarantee the passivity performance. This performance not only depends on the upper bound of the time-varying leakage delay but also depends on the upper bound of the derivative of the time-varying leakage delay . While estimating the upper bound of derivative of the Lyapunov-Krasovskii functional, the discrete and distributed delays should be treated so as to appropriately develop less conservative results. Two numerical examples are given to show the validity and potential of the developed criteria.

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