scholarly journals New Delay-Range-Dependent Robust Exponential Stability Criteria of Uncertain Impulsive Switched Linear Systems with Mixed Interval Nondifferentiable Time-Varying Delays and Nonlinear Perturbations

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Piyapong Niamsup ◽  
Narongsak Yotha ◽  
Kanit Mukdasai
Keyword(s):  
Exponential Stability ◽  
Linear Systems ◽  
Continuous Functions ◽  
Linear Matrix ◽  
Time Varying ◽  
Nonlinear Perturbations ◽  
Stability Criteria ◽  
Parameter Uncertainties ◽  
Robust Exponential Stability ◽  
Switched Linear Systems

We investigate the problem of robust exponential stability analysis for uncertain impulsive switched linear systems with time-varying delays and nonlinear perturbations. The time delays are continuous functions belonging to the given interval delays, which mean that the lower and upper bounds for the time-varying delays are available, but the delay functions are not necessary to be differentiable. The uncertainties under consideration are nonlinear time-varying parameter uncertainties and norm-bounded uncertainties, respectively. Based on the combination of mixed model transformation, Halanay inequality, utilization of zero equations, decomposition technique of coefficient matrices, and a common Lyapunov functional, new delay-range-dependent robust exponential stability criteria are established for the systems in terms of linear matrix inequalities (LMIs). A numerical example is presented to illustrate the effectiveness of the proposed method.

New delay-range-dependent robust exponential stability criteria for uncertain linear systems with discrete interval and distributed time-varying delays and nonlinear perturbations

2015 ◽  
Vol 08 (03) ◽  
pp. 1550061
Author(s):  
Pornthip Somchai ◽  
Kanit Mukdasai
Keyword(s):  
Exponential Stability ◽  
Linear Systems ◽  
Time Varying ◽  
Nonlinear Perturbations ◽  
Stability Criteria ◽  
Robust Exponential Stability ◽  
Time Varying Delay ◽  
Discrete Interval ◽  
Uncertain Linear Systems ◽  
Varying Delay

In this paper, we investigate the problem of robust exponential stability analysis for uncertain linear systems with discrete interval time-varying delay, distributed time-varying delay and nonlinear perturbations. Based on constructing an augmented Lyapunov–Krasovskii functional with some parameter, decomposition technique of coefficient matrix, mixed model transformation with Leibniz–Newton formula and utilization of zero equations, new delay-range-dependent robust exponential stability criteria are derived in terms of linear matrix inequalities (LMIs). Numerical examples are given to show the superiority of our results to those in the literature.

scholarly journals New Delay-Dependent Robust Exponential Stability Criteria of LPD Neutral Systems with Mixed Time-Varying Delays and Nonlinear Perturbations

2013 ◽  
Vol 2013 ◽  
pp. 1-18 ◽  
Author(s):  
Sirada Pinjai ◽  
Kanit Mukdasai
Keyword(s):  
Exponential Stability ◽  
Coefficient Matrix ◽  
Linear Matrix ◽  
Time Varying ◽  
Nonlinear Perturbations ◽  
Stability Criteria ◽  
Neutral Systems ◽  
Robust Exponential Stability ◽  
Delay Dependent ◽  
Parameter Dependent

This paper is concerned with the problem of robust exponential stability for linear parameter-dependent (LPD) neutral systems with mixed time-varying delays and nonlinear perturbations. Based on a new parameter-dependent Lyapunov-Krasovskii functional, Leibniz-Newton formula, decomposition technique of coefficient matrix, free-weighting matrices, Cauchy’s inequality, modified version of Jensen’s inequality, model transformation, and linear matrix inequality technique, new delay-dependent robust exponential stability criteria are established in terms of linear matrix inequalities (LMIs). Numerical examples are given to show the effectiveness and less conservativeness of the proposed methods.

scholarly journals Robust Exponential Stability Criteria of LPD Systems with Mixed Time-Varying Delays and Nonlinear Perturbations

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Kanit Mukdasai ◽  
Akkharaphong Wongphat ◽  
Piyapong Niamsup
Keyword(s):  
Exponential Stability ◽  
Linear Matrix ◽  
Time Varying ◽  
Nonlinear Perturbations ◽  
Matrix Inequalities ◽  
Stability Criteria ◽  
Robust Exponential Stability ◽  
The Stability ◽  
Delay Dependent ◽  
Parameter Dependent

This paper investigates the problem of robust exponential stability for linear parameter-dependent (LPD) systems with discrete and distributed time-varying delays and nonlinear perturbations. Parameter dependent Lyapunov-Krasovskii functional, Leibniz-Newton formula, and linear matrix inequality are proposed to analyze the stability. On the basis of the estimation and by utilizing free-weighting matrices, new delay-dependent exponential stability criteria are established in terms of linear matrix inequalities (LMIs). Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.

DELAY-DEPENDENT ROBUST EXPONENTIAL STABILITY FOR UNCERTAIN RECURRENT NEURAL NETWORKS WITH TIME-VARYING DELAYS

2007 ◽  
Vol 17 (03) ◽  
pp. 207-218 ◽  
Author(s):  
BAOYONG ZHANG ◽  
SHENGYUAN XU ◽  
YONGMIN LI
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Recurrent Neural Networks ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Robust Exponential Stability ◽  
Neuron Activation ◽  
Exponentially Stable

This paper considers the problem of robust exponential stability for a class of recurrent neural networks with time-varying delays and parameter uncertainties. The time delays are not necessarily differentiable and the uncertainties are assumed to be time-varying but norm-bounded. Sufficient conditions, which guarantee that the concerned uncertain delayed neural network is robustly, globally, exponentially stable for all admissible parameter uncertainties, are obtained under a weak assumption on the neuron activation functions. These conditions are dependent on the size of the time delay and expressed in terms of linear matrix inequalities. Numerical examples are provided to demonstrate the effectiveness and less conservatism of the proposed stability results.

Global Robust Exponential Stability of Cohen-Grossberg Neural Network with Time Varying Delays

2012 ◽  
Vol 182-183 ◽  
pp. 1135-1140 ◽  
Author(s):  
Rui Zhang ◽  
Chang Tao Wang
Keyword(s):  
Neural Network ◽  
Exponential Stability ◽  
Functional Method ◽  
Jensen Inequality ◽  
Linear Matrix ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Robust Exponential Stability ◽  
Inequality Technique ◽  
Global Robust Exponential Stability

In this paper, the global robust exponential stability is discussed for Cohen-Grossgerg neural network with parameter uncertainties and time varying delays. On the basis of the linear matrix inequalities (LMIs) technique, and Lyapunov functional method combined with the Bellman inequality and Jensen inequality technique, we have obtained the main condition to ensure the global robust exponential stability of the equilibrium point for this system. The proposed result is less restrictive, easier to check in practice. Remarks are made with other previous works to show the superiority of the obtained result, and the simulation example is used to demonstrate the effectiveness of our result.

scholarly journals New Robust Exponential Stability Criterion for Uncertain Neutral Systems with Discrete and Distributed Time-Varying Delays and Nonlinear Perturbations

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Sirada Pinjai ◽  
Kanit Mukdasai
Keyword(s):  
Exponential Stability ◽  
Model Transformation ◽  
Sufficient Conditions ◽  
Coefficient Matrix ◽  
Linear Matrix ◽  
Time Varying ◽  
Nonlinear Perturbations ◽  
Matrix Inequalities ◽  
Neutral Systems ◽  
Robust Exponential Stability

We investigate the problem of robust exponential stability for uncertain neutral systems with discrete and distributed time-varying delays and nonlinear perturbations. Based on the combination of descriptor model transformation, decomposition technique of coefficient matrix, and utilization of zero equation and new Lyapunov functional, sufficient conditions for robust exponential stability are obtained and formulated in terms of linear matrix inequalities (LMIs). The new stability conditions are less conservative and more general than some existing results.

scholarly journals Improved Stability Criteria on Linear Systems with Distributed Interval Time-Varying Delays and Nonlinear Perturbations

Computation ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 22
Author(s):  
Jitsin Piyawatthanachot ◽  
Narongsak Yotha ◽  
Kanit Mukdasai
Keyword(s):  
Linear Systems ◽  
Model Transformation ◽  
Linear Matrix ◽  
Time Varying ◽  
Nonlinear Perturbations ◽  
Matrix Inequalities ◽  
Stability Criteria ◽  
Decomposition Approach ◽  
Improved Stability ◽  
Delay Decomposition Approach

The problem of delay-range-dependent stability analysis for linear systems with distributed time-varying delays and nonlinear perturbations is studied without using the model transformation and delay-decomposition approach. The less conservative stability criteria are obtained for the systems by constructing a new augmented Lyapunov–Krasovskii functional and various inequalities, which are presented in terms of linear matrix inequalities (LMIs). Four numerical examples are demonstrated for the results given to illustrate the effectiveness and improvement over other methods.

scholarly journals ℋ∞Performance and Stability Analysis of Linear Systems with Interval Time-Varying Delays and Stochastic Parameter Uncertainties

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
M. J. Park ◽  
O. M. Kwon ◽  
Ju H. Park ◽  
S. M. Lee ◽  
E. J. Cha
Keyword(s):  
Stability Analysis ◽  
Linear Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Parameter Uncertainties ◽  
Interval Time ◽  
Stochastic Parameter ◽  
Stochastic Properties ◽  
Random Change

This paper deals with the problems ofℋ∞performance and stability analysis for linear systems with interval time-varying delays. It is assumed that the parameter uncertainties are of stochastic properties to represent random change of various environments. By constructing a newly augmented Lyapunov-Krasovskii functional, less conservative criteria of the concerned systems are introduced with the framework of linear matrix inequalities (LMIs). Four numerical examples are given to show the improvements over the existing ones and the effectiveness of the proposed methods.

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