Myeong-Jin Park

Stability of time-delay systems via Wirtinger-based double integral inequality

Based on the Wirtinger-based integral inequality, a double integral form of the Wirtinger-based integral inequality (hereafter called as Wirtinger-based double integral inequality) is introduced in this paper. To show the effectiveness of the proposed inequality, two stability criteria for systems with discrete and distributed delays are derived within the framework of linear matrix inequalities (LMIs). The advantage of employing the proposed inequalities is illustrated via two numerical examples.

Extended Dissipative Analysis for Neural Networks With Time-Varying Delays

In this brief, an extended dissipativity analysis was conducted for a neural network with time-varying delays. The concept of the extended dissipativity can be used to solve for the H∞, L2 - L∞, passive, and dissipative performance by adjusting the weighting matrices in a new performance index. In addition, the activation function dividing method is modified by introducing a tuning parameter. Examples are provided to show the effectiveness and less conservatism of the proposed method.

Synchronization criteria for coupled stochastic neural networks with time-varying delays and leakage delay

Abstract This paper proposes new delay-dependent synchronization criteria for coupled stochastic neural networks with time-varying delays and leakage delay. By constructing a suitable Lyapunov–Krasovskiis functional and utilizing Finslers lemma, novel synchronization criteria for the networks are established in terms of linear matrix inequalities (LMIs) which can be easily solved by using the LMI toolbox in MATLAB. Three numerical examples are given to illustrate the effectiveness of the proposed methods.

Improved results on stability of linear systems with time-varying delays via Wirtinger-based integral inequality

Abstract In this paper, the problem of stability analysis for linear systems with time-varying delays is considered. By the consideration of new augmented Lyapunov functionals, improved delay-dependent stability criteria for asymptotic stability of the system are proposed for two cases of conditions on time-varying delays with the framework of linear matrix inequalities (LMIs), which can be solved easily by various efficient convex optimization algorithms. The enhancement of the feasible region of the proposed criteria is shown via three numerical examples by the comparison of maximum delay bounds.

Stability and stabilization for discrete-time systems with time-varying delays via augmented Lyapunov–Krasovskii functional

Abstract This paper is concerned with the stability and stabilization problems for discrete-time systems with interval time-varying delays. By construction of an augmented Lyapunov–Krasovskii functional and utilization of zero equalities, improved delay-dependent criteria for asymptotic stability of the systems are derived in terms of linear matrix inequalities (LMIs). Based on the proposed stability criteria, a sufficient condition for designing feedback gains of time-delayed controllers which guarantee the stability of the concerned system is presented. Through three numerical examples, the effectiveness to enhance the feasible region of the proposed criteria is demonstrated.

A new augmented Lyapunov–Krasovskii functional approach for stability of linear systems with time-varying delays

Abstract This paper proposes improved delay-dependent conditions for asymptotic stability of linear systems with time-varying delays. The proposed method employs a suitable Lyapunov–Krasovskii’s functional for new augmented system. Based on Lyapunov method, delay-dependent stability criteria for the systems are established in terms of linear matrix inequalities (LMIs) which can be easily solved by various optimization algorithms. Three numerical examples are included to show that the proposed method is effective and can provide less conservative results.

Augmented Lyapunov--Krasovskii functional approaches to robust stability criteria for uncertain Takagi--Sugeno fuzzy systems with time-varying delays

This paper considers the problem of robust stability analysis for uncertain Takagi-Sugeno (T-S) fuzzy systems with time-varying delays. By constructing an augmented Lyapunov-Krasovskii functional and utilizing Finslers Lemma, a novel criterion for delay-dependent robust stability of T-S fuzzy model with time-varying delay is derived in terms of linear matrix inequalities (LMIs). Also, a further improved stability criterion is proposed by utilizing free weighting techniques. Finally, three numerical examples are included to show the superiority of the proposed criteria.

New delay-partitioning approaches to stability criteria for uncertain neutral systems with time-varying delays

In this paper, the problem of stability analysis for uncertain neutral systems with time-varying delays is considered. The parameter uncertainties are assumed to be norm-bounded. By use of new augmented Lyapunov functional and delay-partitioning techniques, delay-dependent stability criteria to guarantee the asymptotic stability are established in terms of linear matrix inequalities (LMIs), which can be solved easily by various efficient convex optimization algorithms. Four numerical examples are given to show the superiority of the proposed methods.

On stability criteria for neural networks with time-varying delay using Wirtinger-based multiple integral inequality

Abstract This paper investigates the problem of delay-dependent stability analysis of neural networks with time-varying delay. Based on Wirtinger-based integral inequality which suggests very closed lower bound of Jensens inequality, a new Wirtinger-based multiple integral inequality is presented and it is applied to time-varying delayed neural networks by using reciprocally convex combination approach of high order cases. Three numerical examples are given to describe the less conservatism of the proposed methods.

New criteria on delay-dependent stability for discrete-time neural networks with time-varying delays

In this paper, the problem of delay-dependent stability for discrete-time neural networks with time-varying delays is investigated. By constructing a newly augmented Lyapunov-Krasovskii functional, a sufficient condition for guaranteeing the asymptotic stability of the concerned network is derived in the framework of linear matrix inequalities. Also, a further improved stability condition is developed by proposing a new activation condition which has not been considered in the literature. Two numerical examples are given to illustrate the effectiveness of the proposed methods.