Hong-Bing Zeng

Free-Matrix-Based Integral Inequality for Stability Analysis of Systems With Time-Varying Delay

The free-weighting matrix and integral-inequality methods are widely used to derive delay-dependent criteria for the stability analysis of time-varying-delay systems because they avoid both the use of a model transformation and the technique of bounding cross terms. This technical note presents a new integral inequality, called a free-matrix-based integral inequality, that further reduces the conservativeness in those methods. It includes well-known integral inequalities as special cases. Using it to investigate the stability of systems with time-varying delays yields less conservative delay-dependent stability criteria, which are given in terms of linear matrix inequalities. Two numerical examples demonstrate the effectiveness and superiority of the method.

New results on stability analysis for systems with discrete distributed delay

The integral inequality technique is widely used to derive delay-dependent conditions, and various integral inequalities have been developed to reduce the conservatism of the conditions derived. In this study, a new integral inequality was devised that is tighter than existing ones. It was used to investigate the stability of linear systems with a discrete distributed delay, and a new stability condition was established. The results can be applied to systems with a delay belonging to an interval, which may be unstable when the delay is small or nonexistent. Three numerical examples demonstrate the effectiveness and the smaller conservatism of the method.

Passivity analysis for neural networks with a time-varying delay

This paper deals with the problem of passivity analysis for neural networks with both time-varying delay and norm-bounded parameter uncertainties by employing an improved free-weighting matrix approach. Some useful terms have been retained, which were used to be ignored in the derivative of Lyapunov-Krasovskii functional. Furthermore, the relationship among the time-varying delay, its upper bound and their difference is taken into account. As a result, for two types of time-varying delays, less conservative delay-dependent passivity conditions are obtained in terms of linear matrix inequalities (LMIs), respectively. Finally, a numerical example is given to demonstrate the effectiveness of the proposed techniques.

Stability analysis of systems with time-varying delay via relaxed integral inequalities

Abstract This paper investigates the stability of linear systems with a time-varying delay. The key problem concerned is how to effectively estimate single integral term with time-varying delay information appearing in the derivative of Lyapunov–Krasovskii functional. Two novel integral inequalities are developed in this paper for this estimation task. Compared with the frequently used inequalities based on the combination of Wirtinger-based inequality (or Auxiliary function-based inequality) and reciprocally convex lemma, the proposed ones can provide smaller bounding gap without requiring any extra slack matrix. Four stability criteria are established by applying those inequalities. Based on three numerical examples, the advantages of the proposed inequalities are illustrated through the comparison of maximal admissible delay bounds provided by different criteria.

Robust passivity analysis of neural networks with discrete and distributed delays

This paper focuses on the problem of passivity of neural networks in the presence of discrete and distributed delay. By constructing an augmented Lyapunov functional and combining a new integral inequality with the reciprocally convex approach to estimate the derivative of the Lyapunov-Krasovskii functional, sufficient conditions are established to ensure the passivity of the considered neural networks, in which some useful information on the neuron activation function ignored in the existing literature is taken into account. Three numerical examples are provided to demonstrate the effectiveness and the merits of the proposed method.

Stability analysis of generalized neural networks with time-varying delays via a new integral inequality

This paper focuses on the delay-dependent stability of a class of generalized neural networks (NNs) with time-varying delays. A free-matrix-based inequality is presented by introducing a set of slack variables, which encompasses the Wirtinger-based inequality as a special case. Then, by constructing a suitable Lyapunov-Krasovskii functional and utilizing the new inequality to bound the derivative of the Lyapunov-Krasovskii functional, some sufficient conditions are derived to assure the stability of the considered neural networks. Three numerical examples are provided to demonstrate the effectiveness and the significant improvement of the proposed method.

Delay-Variation-Dependent Stability of Delayed Discrete-Time Systems

This note is concerned with the stability analysis of linear discrete-time system with a time-varying delay. A generalized free-weighting-matrix (GFWM) approach is proposed to estimate summation terms in the forward difference of Lyapunov functional, and theoretical study shows that the GFWM approach encompasses several frequently used estimation approaches as special cases. Moreover, an augmented Lyapunov functional with a delay-product type term is constructed to take into account delay changing information. As a result, the proposed GFWM approach, together with the augmented Lyapunov functional, leads to a less conservative delay-variation-dependent stability criterion. Finally, numerical examples are given to illustrate the advantages of the proposed criterion.

Improved Delay-dependent Robust Stability Analysis for Neutral-type Uncertain Neural Networks with Markovian jumping Parameters and Time-varying Delays

Abstract This paper deals with the problem of robust stochastic stability analysis for a class of neutral-type uncertain neural networks with Markovian jumping parameters and time-varying delays. By introducing an novel mode-dependent Augmented Lyapunov-Krasovskii functional with delay partitioning and Wirtinger-based integral inequality techniques, some improved delay-dependent stochastically stable conditions are proposed in the form of LMIs. Numerical simulations are provided to show the effectiveness and less conservatism of the results.

Dissipativity analysis of neural networks with time-varying delays

This paper focuses on the problem of delay-dependent dissipativity analysis for a class of neural networks with time-varying delays. A free-matrix-based inequality method is developed by introducing a set of slack variables, which can be optimized via existing convex optimization algorithms. Then, by employing Lyapunov functional approach, sufficient conditions are derived to guarantee that the considered neural networks are strictly ( Q , S , R ) -γ-dissipative. The conditions are presented in terms of linear matrix inequalities and can be readily checked and solved. Numerical examples are finally provided to demonstrate the effectiveness and advantages of the proposed new design techniques.

Summation Inequalities to Bounded Real Lemmas of Discrete-Time Systems With Time-Varying Delay

Summation inequality is an important technique for analysis of discrete-time systems with a time-varying delay. It seems that from the literature a tighter inequality usually leads to a less conservative criterion. Based on