A. Arunkumar

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.

Robust sampled-data H∞ control for mechanical systems

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 state estimation for discrete-time BAM neural networks with time-varying delay

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.

Robust reliable sampled-data H∞ control for uncertain stochastic systems with random delay

In this article, the problem of robust reliable sampled-data H∞ control for a class of uncertain nonlinear stochastic system with random delay control input against actuator failures has been studied. In the considered system, the parameter uncertainty satisfies the norm bounded condition and the involved time delay in control input are assumed to be randomly time-varying which is modeled by introducing Bernoulli distributed sequences. By constructing a novel Lyapunov-Krasovskii functional involving with the lower and upper bounds of the delay, a new set of sufficient conditions are derived in terms of linear matrix inequalities LMIs for ensuring the robust asymptotic stability of the uncertain nonlinear stochastic system with random delay and disturbance attenuation level γ>0 about its equilibrium point for all possible actuator failures. In particular, Schur complement together with Jensons integral inequality is utilized to substantially simplify the derivation in the main results. The derived analytic results are applied to design robust reliable sampled-data H∞ controller for hanging crane structure model and simulation results are provided to demonstrate the effectiveness of the proposed control law.

Robust reliable H∞ control for fuzzy systems with random delays and linear fractional uncertainties

This article studies the reliable robust stabilization problem for a class of uncertain Takagi-Sugeno (TS) fuzzy systems with time-varying delays. The delay factor is assumed to be random delay which belongs to a given interval and parameter uncertainties are considered with linear fractional transformation form. By implementing a proper novel Lyapunov functional together with linear matrix inequality (LMI) approach, a new set of delay-dependent sufficient conditions is derived to guarantee the asymptotic stability of TS fuzzy system with a prescribed H ∞ performance index. Further, a reliable robust H ∞ control design with an appropriate gain matrix has been derived to achieve the robust asymptotic stability for uncertain TS fuzzy system. Further, Schur complement and Jensens integral inequality are used to simplify the derivation in the main results. The set of sufficient conditions is established using the relationship among the random time-varying delay and its lower and upper bounds, which can be easily solved by MATLAB LMI toolbox. Finally, an illustrative example based on the truck-trailer model is provided to show the effectiveness of the proposed new design technique.

Robust reliable H∞ control for stochastic neural networks with randomly occurring delays

Abstract This paper investigates the problem of robust stabilization for a class of discrete-time stochastic neural networks with randomly occurring discrete and distributed time-varying delays. More precisely, the neuron activation functions are assumed to be more general and satisfy sector-like nonlinearities. Moreover, the effects of both variation range and probability distribution of mixed time-delays are taken into consideration in the proposed problem. The main objective of this paper is to design a state feedback reliable H ∞ controller such that for all admissible uncertainties as well as actuator failure cases, the resulting closed-loop form of considered neural network is robustly asymptotically stable while satisfying a prescribed H ∞ performance constraint. Linear matrix inequality approach together with proper construction of Lyapunov–Krasovskii functional is employed for obtaining delay dependent sufficient conditions for the existence of robust reliable H ∞ controller. The obtained results are formulated in terms of linear matrix inequalities (LMIs) which can be easily solved by using the MATLAB LMI toolbox. Finally, a numerical example with simulation results is provided to illustrate the effectiveness of the obtained control law and less conservativeness of the proposed results.

New LMI-Based Passivity Criteria for Neutral-Type BAM Neural Networks with Randomly Occurring Uncertainties

In this paper, we study the passivity analysis for a class of neutral-type BAM neural networks with time-varying delays and randomly occurring uncertainties as well as generalized activation functions. Linear matrix inequality (LMI) approach together with the construction of proper Lyapunov–Krasovskii functional involving triple integrals and augmented type constraint is implemented to derive a new set of sufficient conditions for obtaining the required result. More precisely, first we derive the passivity condition for BAM neural networks without uncertainties and then the result is extended to the case with randomly occurring uncertainties. In particular, the presented results depend not only upon discrete delay but also distributed time varying delay. The obtained passivity conditions are formulated in terms of linear matrix inequalities that can be easily solved by using the MATLAB-LMI toolbox. Finally, the effectiveness of the proposed passivity criterion is demonstrated through numerical example.

Reliable gain-scheduled control design for networked control systems

In this article, the problem of reliable gain-scheduled H∞ performance optimization and controller design for a class of discrete-time networked control system NCS is discussed. The main aim of this work is to design a gain-scheduled controller, which consists of not only the constant parameters but also the time-varying parameter such that NCS is asymptotically stable. In particular, the proposed gain-scheduled controller is not only based on fixed gains but also the measured time-varying parameter. Further, the result is extended to obtain a robust reliable gain-scheduled H∞ control by considering both unknown disturbances and linear fractional transformation parametric uncertainties in the system model. By constructing a parameter-dependent Lyapunov-Krasovskii functional, a new set of sufficient conditions are obtained in terms of linear matrix inequalities LMIs. The existence conditions for controllers are formulated in the form of LMIs, and the controller design is cast into a convex optimization problem subject to LMI constraints. Finally, a numerical example based on a station-keeping satellite system is given to demonstrate the effectiveness and applicability of the proposed reliable control law.

Robust Passivity of Fuzzy Cohen-Grossberg Neural Networks with Time-Varying Delays

In this paper the problem of robust passivity analysis for a class of fuzzy Cohen-Grossberg neural networks with time varying delay is considered. By employing the Lyapunov technique and linear matrix inequality approach, delay independent criterion’s are established for the robust passivity of fuzzy Cohen-Grossberg neural networks. The results are expressed in terms of LMIs, which can be easily solved by the MATLAB LMI toolbox. Finally, a numerical example is given to illustrate the effectiveness of the proposed results.