K. Mathiyalagan

Design of state estimator for bidirectional associative memory neural networks with leakage delays

This paper considers the issue of state estimation for a class of bidirectional associative memory (BAM) neural networks. More precisely, the BAM model is considered with mixed delays which includes a constant delay in the leakage term, time-varying discrete delay and constant distributed delay. By constructing a novel Lyapunov-Krasovskii functional (LKF) together with free-weighting matrix technique, a new delay dependent sufficient condition is derived to estimate the neuron states through available output measurements such that, for all admissible delay bounds, the resulting estimation error system is globally asymptotically stable. Also it is assumed that the derivative of time delay is not necessarily zero or less than one. Further the derived conditions are formulated in terms of a set of linear matrix inequalities (LMIs) which can be easily solved by using some standard numerical packages. Finally a numerical example with simulation result is presented to show the effectiveness of the proposed theory. The result reveals that the leakage delays have a destabilizing influence on the system and they cannot be ignored.

Robust passivity analysis of fuzzy Cohen–Grossberg BAM neural networks with time-varying delays

Abstract This paper is concerned with the problem of passivity analysis for a class of Cohen–Grossberg fuzzy bidirectional associative memory (BAM) neural networks with time varying delay. By employing the delay fractioning technique and linear matrix inequality optimization approach, delay dependent passivity criteria are established that guarantees the passivity of fuzzy Cohen–Grossberg BAM neural networks with uncertainties. The passivity condition is expressed in terms of LMIs, which can be easily solved by various convex optimization algorithms. Finally, a numerical example is given to illustrate the effectiveness of the proposed result.

Reliable Mixed

This paper is concerned with the problem of reliable mixed H∞ and passivity-based control for a class of stochastic Takagi-Sugeno (TS) fuzzy systems with Markovian switching and probabilistic time varying delays. Different from the existing works, the H∞ and passivity control problem with probabilistic occurrence of time-varying delays and actuator failures is considered in a unified framework, which is more general in some practical situations. The main aim of this paper is to design a reliable mixed H∞ and passivity-based controller such that the stochastic TS fuzzy system with Markovian switching is stochastically stable with a prescribed mixed H∞ and passivity performance level γ > 0. Based on the Lyapunov-Krasovskii functional (LKF) involving lower and upper bound of probabilistic time delay and convex combination technique, a new set of delay-dependent sufficient condition in terms of linear matrix inequalities (LMIs) is established for obtaining the required result. Finally, a numerical example based on the modified truck-trailer model is given to demonstrate the effectiveness and applicability of the proposed design techniques.

H_\infty

Abstract This paper addresses the problem of admissibility analysis, and mixed H ∞ and passive control synthesis for a class of singular systems with Markovian jumps and time delays. By implementing an appropriate Lyapunov–Krasovskii functional together with Wirtinger-based inequality, a new set of delay dependent sufficient condition is derived in terms of linear matrix inequalities which guarantees that the singular Markovian jump system is regular, impulse-free and stochastically stable. In particular, the delay factor is assumed to be either constant or time varying, and either differentiable or non-differentiable. Also, it is noted that the proposed stochastic admissibility criteria are delay dependent in general and delay derivative dependent when the delay is differentiable. Further, mixed H ∞ and passive control design with an appropriate gain matrix has been derived to achieve the stabilization for singular systems in the presence of differentiable as well as non-differentiable time varying delays. More precisely, when the proposed LMIs are feasible, an expression for a desired mixed H ∞ and passive control will be determined. Also, as special cases different control systems such as H ∞ and passivity control process can be achieved for the considered systems with the proposed design procedure. Finally, several numerical examples including DC motor driving model are given to verify the effectiveness of the proposed design technique.

and Passivity-Based Control for Fuzzy Markovian Switching Systems With Probabilistic Time Delays and Actuator Failures

In this paper, the stability analysis and control design of Takagi–Sugeno (TS) fuzzy neural networks with various activation functions and continuously distributed time delays are addressed. By implementing the delay-fractioning technique together with the linear matrix inequality (LMI) approach , a new set of sufficient conditions is derived in terms of linear matrix inequalities, which ensure the stability of the considered fuzzy neural networks. Further, based on the above-mentioned techniques, a control law with an appropriate gain control matrix is derived to achieve stabilization of the fuzzy neural networks. In addition, the results are extended to the study of the stability and stabilization results for TS fuzzy uncertain neural networks with parameter uncertainties. The stabilization criteria are obtained in terms LMIs and hence the gain control matrix can be easily determined by the MATLAB LMI control toolbox. Two numerical examples with simulation results are given to illustrate the effectiveness of the obtained result.

Mixed H∞ and passive control for singular Markovian jump systems with time delays

In this article, the problem of robust stability and stabilisation for a class of uncertain neutral systems with discrete and distributed time delays is considered. By utilising a new Lyapunov functional based on the idea of delay partitioning approach, we employ the linear matrix inequality technique to derive delay-dependent criteria which ensures the robust stability of uncertain neutral systems. The obtained stability conditions are formulated in terms of linear matrix inequalities that can easily be solved by using standard software packages. Further, the result is extended to study the robust stabilisation for uncertain neutral systems with parameter uncertainties. A state feedback controller is proposed to guarantee the robust asymptotic stabilisation for uncertain systems and the controller is constructed in terms of the solution to a set of matrix inequalities. Finally, numerical examples are presented to illustrate the effectiveness and conservatism of the obtained results. It is shown that the results developed in this article can tolerate larger allowable delay than some existing works in the literature. Further, it is proved that the proposed criterion is also computationally less conservative when compared to some existing results.

New stability and stabilization criteria for fuzzy neural networks with various activation functions

This article addresses the issue of robust sampled-data H∞ control for a class of uncertain mechanical systems with input delays and linear fractional uncertainties which appear in all the mass, damping, and stiffness matrices. Then, a novel Lyapunov-Krasovskii functional is constructed to obtain sufficient conditions under which the uncertain mechanical system is robustly, asymptotically stable with disturbance attenuation level γ>0 about its equilibrium point for all admissible uncertainties. More precisely, Schur complement and Jensons integral inequality are utilized to substantially simplify the derivation of the main results. In particular, a set of sampled-data H∞ controller is designed in terms of the solution of certain linear matrix inequalities that can be solved effectively using available MATLAB software. Finally, a numerical example with simulation result is provided to show the effectiveness and less conservativeness of the proposed sampled-data H∞ control scheme.

Robust stability and control for uncertain neutral time delay systems

This paper addresses the problem of controller design for passivity of uncertain fuzzy Hopfield neural networks with time-varying delays. The main purpose of this paper is to design a state feedback fuzzy controller such that the resulting closed-loop system is passive. A new set of sufficient conditions are derived for achieving the required result by employing the Lyapunov functional method and matrix analysis technique. The derived criteria are expressed in terms of linear matrix inequalities that can be easily checked using standard numerical software. Two numerical examples with simulation results are given to illustrate the effectiveness and conservatism of the obtained results.

Robust sampled-data H∞ control for mechanical systems

In this paper, we discussed non-fragile state estimation problem for a class of memristive neural networks with two different types of memductance functions and uncertain time-varying delays. The required results are derived by using a suitable Lyapunov-Krasovskii functional (LKF) and using linear matrix inequality (LMI) approach together with Wirtinger-type inequality analysis. The sufficient conditions are presented for the existence of non-fragile state estimator based on the combined H ∞ and passivity performance criterions. The results are proposed in terms of LMIs, which can guarantee the global asymptotic stability of the error dynamics between the considered memristive RNNs and its non-fragile observer. Finally, a numerical example is presented to illustrate the effectiveness of the theoretical results via simulations.

Design of a passification controller for uncertain fuzzy Hopfield neural networks with time-varying delays

This paper is concerned with the robust delay-dependent state estimation problem for a class of discrete-time Bidirectional Associative Memory (BAM) neural networks with time-varying delays. By using the Lyapunov-Krasovskii functional together with linear matrix inequality (LMI) approach, a new set of sufficient conditions are derived for the existence of state estimator such that the error state system is asymptotically stable. More precisely, an LMI-based state estimator and delay-dependent stability criterion for delayed BAM neural networks are developed. The conditions are established in terms of LMIs which can be solved by the MATLAB LMI toolbox. It should be mentioned that all the sufficient conditions are dependent on the upper and lower bounds of the delays. Also, the desired estimator unknown gain matrix is determined in terms of the solution to these LMIs. Finally, numerical examples with simulation results are given to illustrate the effectiveness and applicability of the obtained results.