M. Syed Ali

Delay-dependent stability criteria of uncertain Markovian jump neural networks with discrete interval and distributed time-varying delays

In this paper, a class of uncertain neural networks with discrete interval and distributed time-varying delays and Markovian jumping parameters (MJPs) are carried out. The Markovian jumping parameters are modeled as a continuous-time, finite-state Markov chain. By using the Lyapunov-Krasovskii functionals (LKFs) and linear matrix inequality technique, some new delay-dependent criteria is derived to guarantee the mean-square asymptotic stability of the equilibrium point. Numerical simulations are given to demonstrate the effectiveness of the proposed method. The results are also compared with the existing results to show the less conservativeness.

New passivity criteria for memristor-based neutral-type stochastic BAM neural networks with mixed time-varying delays

This paper deals with the problem of passivity analysis issue for a class of memristor-based neutral-type stochastic bidirectional associative memory neural networks (MNSBAMNNs) with discrete interval and distributed time-varying delays. By constructing new Lyapunov-Krasovskii functional (LKF) with quadruple integral terms and suitable activation function conditions, some delay-dependent passivity criteria are obtained in the linear matrix inequality (LMI) format. A numerical example is given to demonstrate the effectiveness and superiority of the new scheme.

Stability of Markovian jumping recurrent neural networks with discrete and distributed time-varying delays ☆

Abstract In this paper, global stability of Markovian jumping recurrent neural networks with discrete and distributed delays (MJRNN) is considered. A novel linear matrix inequality (LMI) based stability criterion is obtained by using Lyapunov functional theory to guarantee the asymptotic stability of Markovian jumping recurrent neural networks with discrete and distributed delays. By applying Lyapunov method and some inequality techniques, several sufficient conditions are obtained under which the delayed neural networks are stable. Finally, numerical examples are given to demonstrate the correctness of the theoretical results.

State estimation of T–S fuzzy delayed neural networks with Markovian jumping parameters using sampled-data control ☆

Abstract In this paper, we are concerned with the problem of state estimation of Takagi–Sugeno (T–S) fuzzy delayed neural networks with Markovian jumping parameters via sampled-data control. Based on the fuzzy-model-based control approach and linear matrix inequality (LMI) technique, several novel conditions are derived to guarantee the stability of the suggested system. A new class of Lyapunov functional, which contains integral terms, is constructed to derive delay-dependent stability criteria. Some characteristics of the sampling input delay are proposed based on the input delay approach. Numerical examples are given to illustrate the usefulness and effectiveness of the proposed theoretical results.

Robust stability of stochastic uncertain recurrent neural networks with Markovian jumping parameters and time-varying delays

In this paper, stability of stochastic recurrent neural networks with Markovian jumping parameters and time-varying delays is considered. A novel linear matrix inequality (LMI)-based stability criterion is obtained by using Lyapunov functional theory to guarantee the asymptotic stability of Markovian jumping stochastic recurrent neural networks with norm bounded uncertainties and time-varying delays. To reflect the most dynamical behaviors of the system, both parameter uncertainties and stochastic disturbance are considered, where parameter uncertainties enter into all the system matrices, stochastic disturbances are given in the form of a Brownian motion. The stability conditions are derived using Lyapunov–Krasovskii approach, in combined with the LMI techniques. The delay-dependent stability condition is formulated, in which the restriction of the derivative of the time-varying delay should be 1 is removed. Finally, numerical examples are given to demonstrate the correctness of the theoretical results.In this paper, stability of stochastic recurrent neural networks with Markovian jumping parameters and time-varying delays is considered. A novel linear matrix inequality (LMI)-based stability criterion is obtained by using Lyapunov functional theory to guarantee the asymptotic stability of Markovian jumping stochastic recurrent neural networks with norm bounded uncertainties and time-varying delays. To reflect the most dynamical behaviors of the system, both parameter uncertainties and stochastic disturbance are considered, where parameter uncertainties enter into all the system matrices, stochastic disturbances are given in the form of a Brownian motion. The stability conditions are derived using Lyapunov–Krasovskii approach, in combined with the LMI techniques. The delay-dependent stability condition is formulated, in which the restriction of the derivative of the time-varying delay should be 1 is removed. Finally, numerical examples are given to demonstrate the correctness of the theoretical results.

Novel delay-dependent robust H ∞ control of uncertain systems with distributed time-varying delays

This paper investigates the problem of delay dependent robust H ∞ control for a class of uncertain systems with distributed time-varying delays. The aim is to design a delay-dependent robust H ∞ control which ensures robust asymptotic stability of the system. The Delay derivative dependent robust H ∞ control criteria are obtained in terms of Linear Matrix Inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the proposed method. The results are also compared with the existing results to show the conservativeness.

Stochastic stability of discrete-time uncertain recurrent neural networks with Markovian jumping and time-varying delays ✩

Abstract In this paper, the problem of robust exponential stability analysis of uncertain discrete-time recurrent neural networks with Markovian jumping and time-varying delays is studied. By employing the Lyapunov functional and linear matrix inequality (LMI) approach, a new sufficient criterion is proposed for the global robust exponential stability of discrete-time recurrent neural networks which contain uncertain parameters and Markovian jumping parameters. The obtained stability criterion is characterized in terms of linear matrix inequalities (LMIs) and can be easily checked by utilizing the efficient LMI toolbox. Two numerical examples are presented to show the effectiveness and conservativeness of the proposed method.

Novel H ∞ state estimation of static neural networks with interval time-varying delays via augmented Lyapunov-Krasovskii functional

This paper focuses on studying the H ∞ state estimation of static neural networks with interval time-varying delays via augmented Lyapunov-Krasovskii functional. By constructing a suitable augmented Lyapunov-Krasovskii functional with triple integral terms and linear matrix inequality technique, the delay-dependent criteria are conferred so that the error system is globally asymptotically stable with H ∞ performance. The activation functions are assumed to satisfy sector-like nonlinearities. 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 simulation is given to demonstrate the effectiveness and superiority of the proposed method comparing with some existing results.

Robust finite-time H∞ control for a class of uncertain switched neural networks of neutral-type with distributed time varying delays

In this paper, we investigate finite-time H ∞ control of uncertain switched neural networks of neutral type with distributed time varying delays. The mathematical model of the switched neural networks with distributed delays is established in which a set of neural networks are used as individual subsystems and an arbitrary switching rule is assumed, stability analysis for such switched neural networks is addressed based on the linear matrix inequality (LMI) and finite-time bounded average dwell time approach. Finite-time H ∞ performance analysis was established for switched neural network of neutral type. Numerical examples are given to illustrate the usefulness of our proposed method.

H∞ state estimation of generalised neural networks with interval time-varying delays

ABSTRACT This paper focuses on studying the H∞ state estimation of generalised neural networks with interval time-varying delays. The integral terms in the time derivative of the Lyapunov–Krasovskii functional are handled by the Jensen’s inequality, reciprocally convex combination approach and a new Wirtinger-based double integral inequality. A delay-dependent criterion is derived under which the estimation error system is globally asymptotically stable with H∞ performance. The proposed conditions are represented by linear matrix inequalities. Optimal H∞ norm bounds are obtained easily by solving convex problems in terms of linear matrix inequalities. The advantage of employing the proposed inequalities is illustrated by numerical examples.