A delay decomposition approach to [formula omitted] filter design for stochastic systems with time-varying delay

In this article, the stability analysis for generalized neural networks (GNNs) with a time-varying delay is investigated. About the delay, the differential has only an upper boundary or cannot be obtained. For the both two types of delayed GNNs, up to now, the second-order integral inequalities have been the highest-order integral inequalities utilized to derive the stability conditions. To establish the stability conditions on the basis of the high-order integral inequalities, two challenging issues are required to be resolved. One is the formulation of the Lyapunov-Krasovskii functional (LKF), the other is the high-degree polynomial negative conditions (NCs). By transforming the integrals in N-order generalized free-matrix-based integral inequalities (GFIIs) into the multiple integrals, the hierarchical LKFs are constructed by adopting these multiple integrals. Then, the novel modified matrix polynomial NCs are presented for the 2N-1 degree delay polynomials in the LKF differentials. Thus, the hierarchical linear matrix inequalities (LMIs) are set up and the nonlinear problems caused by the GFIIs are solved at the same time. Eventually, the superiority of the provided hierarchical stability criteria is demonstrated by several numeric examples.

Robust [formula omitted] stabilization for T-S fuzzy systems with time-varying delays and memory sampled-data control

This paper focuses on the further improved stability criteria of uncertain T-S fuzzy systems with time-varying delay by the delay-partitioning approach and a new integral inequality, i.e., the Free-Matrix-Based integral inequality. A modified augmented Lyapunov-Krasovskii functional (LKF) is established by partitioning the delay in all integral terms. Then, new results on tighter bounding inequalities such as Peng-Park's integral inequality (reciprocally convex approach) and the Free-Matrix-based integral inequality (which yields less conservative stability criteria than the Wirtinger-based inequality) are introduced to reduce the enlargement in bounding the derivative of LKF as much as possible, therefore, less conservative results can be expected in terms of esand MIs. Finally, a numerical example is included to show that the proposed conditions are less conservative than existing ones.

This paper addresses the problem of adaptive tracking control for a class of stochastic nonlinear systems with time-varying input delays, and the nonlinear functions of the systems are with not only the unknown parameters but also the unknown state time-varying delays, which is different from the previous work. In this paper, through a state transformation, the system can be easily transformed into a system without the time-varying input delay; the appropriate Lyapunov–Krasovskii functionals are used to compensate the unknown time-varying delay terms, and the quadratic functions instead of the quartic functions often utilized in the existing results are used as Lyapunov functions to analyze the stability of systems and the hyperbolic tangent functions are introduced to deal with the Hessian terms. Fuzzy logic systems (FLSs) in Mamdani type are used to approximate the unknown nonlinear functions. Then, based on the backstepping technique, the adaptive fuzzy controller is designed. The three main advantages of the developed scheme are that (i) unlike the existing results which deal with the nonlinearly parameterized functions by using the separation principle, the nonlinearly parameterized functions are lumped into the continuous functions which can be approximated by using the FLS; (ii) the number of the adjusted parameters only depend on the order of the investigated systems, which can reduce the computational burden greatly; and (iii) the existence of the time-varying input delay such that the controller design becomes much more difficult, and in this paper, it can be dealt with by using an appropriate state transformation. It is proven that all the signals of the closed-loop system are semi-globally uniformly ultimately bounded in probability, whereas the tracking error converges to a small neighborhood of the origin. Finally, simulation results are provided to show the effectiveness of the proposed approach.

Robust fast adaptive fault estimation for systems with time-varying interval delay

Improved stabilization criteria for Takagi–Sugeno fuzzy systems with variable delays

This paper is concerned with $$H_\infty $$Hź state estimation problem of stochastic neural networks with discrete interval and distributed time-varying delays. The time-varying delay is need to be bounded and continuous. By constructing a suitable Lyapunov---Krasovskii functional with triple integral terms and linear matrix inequality technique, the delay-dependent criteria are conferred so that the error system is stochastically asymptotically mean-square stable with $$H_\infty $$Hź performance. The desired estimator gain matrix can be characterized in terms of the solution to linear matrix inequalities, which can be easily solved by some standard numerical algorithms. Numerical simulations are given to demonstrate the effectiveness of the proposed method. The results are also compared with existing methods.

This paper deals with the robust stability for uncertain bidirectional associative memory (BAM) neural networks of neutral-type with time-varying delays. The parameter uncertainties are assumed to be norm bounded, the discrete delays and neutral delays are time-varying delays. The combined method, which is based on the Lyapunov-Krasovskii functional (LKF) combined with some inequality techniques, is used to investigate this problem. Then, by constructing a new LKF, using the Newton-Leibniz formula and introducing some free weighting matrices, some sufficient conditions are proposed to guarantee global asymptotic robust stability for the considered systems. It is also shown that the obtained results can be established in terms of linear matrix inequality (LMI).

Improved result on state estimation for complex dynamical networks with time varying delays and stochastic sampling via sampled-data control

This paper investigates event-triggered <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_{\infty}$</tex> performance state estimation problem for neural networks model with time-varying delays. A novel event-triggered scheme (ETS) introducing the estimation error is designed, which is a tradeoff between the state estimator performance and network communication bandwidth in accordance with practical requirement. A Wirtinger-type free-matrix-based integral inequality (WFMBII) is put forward, in which some delay-product-type matrices are produced to fully link the relationship among time-varying delay and system states. On these basis, sufficient condition is builded to guarantee the estimation error system to be is bounded and satisfies the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H$</tex> ∞ performance requirement. Meanwhile, the desired event-triggered estimators are solved by linear matrix inequalities (LMIs). A numerical example is given to illustrate the correctness of the obtained method.

The delay-dependent stability problem is investigated for discrete-time neural networks with time-varying delays. A new augmented Lyapunov-Krasovskii functional (LKF) with single and double summation terms and several augmented vectors is proposed by decomposing the time-delay interval into two nonequidistant subintervals to derive less conservative stability conditions. Then, by using Wirtinger-based inequality, reciprocally, and extended reciprocally convex combination lemmas, tight estimations for sum terms in the forward difference of the LKF are given. Several zero equalities are introduced to further relax the existing results. Less conservative stability criteria are proposed in terms of linear matrix inequalities (LMIs). Finally, numerical examples are proposed to show the effectiveness and less conservativeness of the proposed method.

This paper is concerned with a new stability criterion for systems with time-varying delays. Firstly, a generalized integral inequality is proposed, which includes some existing inequalities as special cases. Then, a new stability criterion is derived by choosing some new Lyapunov-Krasovskii functionals. Finally, the effectiveness of our method is shown by a numerical example.

Global dissipativity of uncertain discrete-time stochastic neural networks with time-varying delays

The problem of exponentially synchronizing class of delayed neural networks is studied. Both constant and time-varying delays are considered, to obtain the delay-dependent state feedback synchronization gain matrix. By means of the method of Lyapunov–Krasovskii functional, combined with linear matrix inequalities, exponential synchronization of the master–slave structure of neural networks is achieved. The delay interval is decomposed into multiple nonequidistant subintervals, on which Lyapunov–Krasovskii functionals are constructed. On the basis of these functionals, a new exponential synchronization condition, one that is time-delay dependent, is proposed in terms of linear matrix inequalities. A numerical example showing the effectiveness of the proposed method is presented.

This paper is concerned with the stability and the stabilization problem for Takagi–Sugeno (T–S) fuzzy systems with neutral time delays. The sufficient stability conditions are derived using novel Lyapunov–Krasovskii functionals (LKFs). The stability conditions are expressed as linear matrix inequalities (LMIs) and hence easily tractable numerically. These conditions are easily extended to the sufficient conditions for the existence of stabilizing state-feedback fuzzy gains for T–S fuzzy neutral systems with time-varying delays. An example is given to illustrate the effectiveness of the proposed methods.