Global Robust Stability Research Articles

Global robust exponential stability for Hopfield neural networks with non-Lipschitz activation functions

We consider the problem of global robust exponential stability for Hopfield neural networks with norm-bounded parameter uncertainties and inverse Holder neuron activation functions. By using the Brouwer degree properties and some analysis techniques, we investigate the existence and uniqueness of an equilibrium point. Based on the Lyapunov stability theory, we derive a global robust exponential-stability criterion in terms of a linear matrix inequality (LMI). Two numerical examples are provided to demonstrate the efficiency and validity of the proposed robust stability results.

On the Robust Practical Global Stability of Nonlinear Time-varying Systems

The goal of this paper is twofold. The first part presents a Lyapunov statement and proof of the concept of robust global practical exponential stability (RpGES) for nonlinear time varying systems. A RpGES-Lyapunov function for the overall system is exhibited. Its proof is a consequence of some results on converse Lyapunov theorems obtained by Tsinias in 19. The second part provides sufficient conditions for the robust practical globally uniformly asymptotically stability (RpGUAS).

Stability analysis of impulsive parabolic complex networks with multiple time-varying delays

In the present paper, a new impulsive parabolic complex network (IPCN) with time-varying delays is proposed. Then, by constructing appropriate Lyapunov functionals and utilizing inequality techniques, some sufficient conditions are given to ensure that the proposed network model is globally exponentially stable. Furthermore, when the parameter uncertainties appear in the IPCN, several robust global exponential stability conditions are also presented. Finally, two examples with numerical simulations are provided to demonstrate the effectiveness of our criteria.

Global Robust Exponential Stability of Discrete-Time BAM Neural Networks with Time Varying Delays

In this paper, the global robust exponential stability is discussed for discrete-time bidirectional associative memory (BAM) neural networks with time varying delays. By the linear matrix inequality (LMI) technique and discrete Lyapunov functional combined with inequality techniques, a new global exponential stability criterion of the equilibrium point is obtained for this system. The proposed result is less restrictive, and easier to check in practice. Remarks are made with other previous works to show the superiority of the obtained results, and the simulation example is used to demonstrate the effectiveness of our result.

New robust stability results for bidirectional associative memory neural networks with multiple time delays

In this paper, the robust stability problem is investigated for a class of bidirectional associative memory (BAM) neural networks with multiple time delays. By employing suitable Lyapunov functionals and using the upper bound norm for the interconnection matrices of the neural network system, some novel sufficient conditions ensuring the existence, uniqueness and global robust stability of the equilibrium point are derived. The obtained results impose constraint conditions on the system parameters of neural network independent of the delay parameters. Some numerical examples and simulation results are given to demonstrate the applicability and effectiveness of our results, and to compare the results with previous robust stability results derived in the literature.

Stability analysis of impulsive delayed switched systems and applications

In this paper, a general class of impulsive delayed switched systems is considered. By employing the Lyapunov–Razumikhin method and some analysis techniques, we established several global asymptotic stability and global exponential stability criteria for the considered impulsive delayed switched systems, which improve and extend some recent works. As an application, the result of global exponential stability are used to study a class of uncertain linear switched systems with time‐varying delays. Several LMI‐based conditions are proposed to guarantee the global robust stability and global exponential stabilization. The designed memoryless state feedback controller can be easily checked by the LMI toolbox in Matlab. Moreover, the dwell time constraint is imposed for the switching law. Finally, two numerical examples and their simulations are given to show the effectiveness of our proposed results. Copyright © 2012 John Wiley & Sons, Ltd.

Global Robust Exponential Stability of Cohen-Grossberg Neural Network with Time Varying Delays

In this paper, the global robust exponential stability is discussed for Cohen-Grossgerg neural network with parameter uncertainties and time varying delays. On the basis of the linear matrix inequalities (LMIs) technique, and Lyapunov functional method combined with the Bellman inequality and Jensen inequality technique, we have obtained the main condition to ensure the global robust exponential stability of the equilibrium point for this system. The proposed result is less restrictive, easier to check in practice. Remarks are made with other previous works to show the superiority of the obtained result, and the simulation example is used to demonstrate the effectiveness of our result.

Robust stability analysis of interval fuzzy Cohen–Grossberg neural networks with piecewise constant argument of generalized type

In this paper, existence and uniqueness of the solution of interval fuzzy Cohen-Grossberg neural networks with piecewise constant argument are discussed. Based on the comparison principle, it presents new theoretical results on the global robust exponential stability of interval fuzzy Cohen-Grossberg networks with piecewise constant argument. As a special case, the corresponding results of interval fuzzy recurrent neural networks with piecewise constant argument are derived. Three examples are given for illustrating validity of the obtained results.

Robust global stability to delays of a multi-path dual congestion control algorithm

Global stability has been shown for network congestion control algorithms in the absence of propagation delays by use of the conventional Lyapunov function method. When heterogeneous delays are taken into account, this problem becomes harder and is partly answered until the latest work of Papachristodoulou et al., where a Lyapunov–Krasovskii functional argument is used to analyze global stability of nonlinear congestion control algorithms, but only applicable to the single-path case. In this paper, we develop a new multi-path extension to the dual algorithm in the presence of delays. By finding a reasonable Lyapunov–Krasovskii functional candidate, usually difficult to do in a constructive way, we establish a new sufficient condition for robust global stability to delays, which includes Papachristodoulou’s as a special case. Finally, we verify the results through simulations.

Delay-dependent robust stabilization and H∞ control for neural networks with various activation functions

This paper considers the problem of robust stabilization for a class of uncertain neural networks with various activation functions and mixed time delays. The aim is to derive a H∞ control law to ensure the robust stability of the closed-loop system about its equilibrium with parameter uncertainties. By employing the Lyapunov stability theory and the matrix inequality technique, a new set of sufficient conditions is presented for the existence of the H∞ control problem. The stability criteria are derived in terms of linear matrix inequalities (LMIs) which can be solved easily by the Matlab LMI toolbox. In addition to the requirement of global robust stabilization, for a prescribed H∞ performance level the stabilizing controller gain matrices for all delays to satisfy the upper bound of the time-varying delay are required to be obtained. Numerical examples are presented to illustrate the effectiveness of the proposed method.

Robust stability and robust passivity of parabolic complex networks with parametric uncertainties and time-varying delays

In this paper, the robust global exponential stability and robust passivity are investigated for a class of parabolic complex networks with multiple time-varying delays. By constructing appropriate Lyapunov functionals and utilizing inequality techniques, several criteria for robust global exponential stability and robust passivity are established. Finally, a numerical example is also given to illustrate the effectiveness of the obtained results.

Robust μ-stability analysis of Markovian switching uncertain stochastic genetic regulatory networks with unbounded time-varying delays

This paper investigates the global robust stability problem of Markovian switching uncertain stochastic genetic regulatory networks with unbounded time-varying delays and norm bounded parameter uncertainties. The structure variations at discrete time instances during the process of gene regulations known as hybrid genetic regulatory networks based on Markov process is proposed. The jumping parameters considered here are generated from a continuous-time discrete-state homogeneous Markov process, which are governed by a Markov process with discrete and finite state space. The concept of global robust μ-stability in the mean square for genetic regulatory networks is given. Based on Lyapunov function, stochastic theory and Itô’s differential formula, the stability criteria are presented in the form of linear matrix inequalities (LMIs). Numerical examples are presented to demonstrate the effectiveness of the main result.

Parameter-dependent robust stability of uncertain neural networks with time-varying delay

This paper is concerned with the problem of global robust asymptotic stability for delayed neural networks with polytopic parameter uncertainties and time-varying delay. A delay-dependent and parameter-dependent robust stability criterion for the equilibrium of delayed neural networks in the face of polytopic type uncertainties is presented by using a parameter-dependent Lyapunov functional and taking the relationship between the terms in the Leibniz–Newton formula into account. This criterion, expressed as a set of linear matrix inequalities, requires no matrix variable to be fixed for the entire uncertainty polytope, which produces a less conservative stability result.

Global Robust Exponential Stability Analysis for Interval Neural Networks with Mixed Delays

A class of interval neural networks with time‐varying delays and distributed delays is investigated. By employing H‐matrix and M‐matrix theory, homeomorphism techniques, Lyapunov functional method, and linear matrix inequality approach, sufficient conditions for the existence, uniqueness, and global robust exponential stability of the equilibrium point to the neural networks are established and some previously published results are improved and generalized. Finally, some numerical examples are given to illustrate the effectiveness of the theoretical results.

LMI‐Based Approach for Exponential Robust Stability of High‐Order Hopfield Neural Networks with Time‐Varying Delays

This paper studies the problems of global exponential robust stability of high‐order hopfield neural networks with time‐varying delays. By employing a new Lyapunov‐Krasovskii functional and linear matrix inequality, some criteria of global exponential robust stability for the high‐order neural networks are established, which are easily verifiable and have a wider adaptive.

Robust H∞ control for uncertain discrete-time stochastic neural networks with time-varying delays

In the last few years, the H∞ control problem has attracted much attention because of its both practical and theoretical importance. This study presents a robust H∞ control design approach for a class of uncertain discrete-time stochastic neural networks with time-varying delays. The neural network under consideration is subject to time-varying and norm bounded parameter uncertainties. For the robust stabilisation problem, a state feedback controller is designed to ensure global robust stability of the closed-loop form of neural network about its equilibrium point for all admissible uncertainties. In addition, to the requirement of the global robust stability, a prescribed H∞ performance level for all delays to satisfy both the lower bound and upper bound of the interval time-varying delay is required to be obtained. Through construction of a new Lyapunov–Krasovskii functional, a robust H∞ control scheme is presented in terms of linear matrix inequalities (LMIs). The controller gains can be derived by solving a set of LMIs. Finally, numerical examples with simulation results are given to illustrate the effectiveness of the developed theoretical results.

Quantised feedback stabilisation of planar systems via switching-based sliding-mode control

This study is concerned with the feedback stabilisation problem for planar systems in the presence of saturating quantised state measurements. A novel switching-based sliding mode quantised feedback control design method is developed. First, by the introduction of two additional switching lines, a partition of the state space, which is composed of several sector sets, is formed. Then the adjustment policy of the quantisation parameter is developed in each sector set. With the designed discrete online adjustment of the quantisation parameter, the proposed quantised feedback control strategy can drive the state trajectories to the desired switching line in finite time and then global robust stabilisation of the closed-loop system is guaranteed. Finally, an illustrative example is given to verify the validity of the theoretical results.

Saturated Output-Feedback control of continuous anaerobic digestors

The saturated Output-Feedback (OF) control problem for a class of four-state anaerobic digestors with volatile fatty acids (VFAs) measurement is addressed. The reactor must operate about an optimal steady-state, with maximum VFA consumption, that is locally stable but not structurally unstable. The problem is addressed as an interlaced control-observer design within a geometric control framework in the light of passivity, observability, and bifurcation properties. The result is a saturated linear PI OF controller with global robust stability conditions in terms of control gains and limits. The proposed approach is illustrated with a representative case example through numerical simulations.

Further analysis of global robust stability of neural networks with multiple time delays

This paper deals with the problem of the global robust asymptotic stability of the class of dynamical neural networks with multiple time delays. We propose a new alternative sufficient condition for the existence, uniqueness and global asymptotic stability of the equilibrium point under parameter uncertainties of the neural system. We first prove the existence and uniqueness of the equilibrium point by using the Homomorphic mapping theorem. Then, by employing a new Lyapunov functional, the Lyapunov stability theorem is used to establish the sufficient condition for the asymptotic stability of the equilibrium point. The obtained condition is independent of time delays and relies on the network parameters of the neural system only. Therefore, the equilibrium and stability properties of the delayed neural network can be easily checked. We also make a detailed comparison between our result and the previous corresponding results derived in the previous literature. This comparison proves that our result is new and improves some of the previously reported robust stability results. Some illustrative numerical examples are given to show the applicability and advantages of our result.

Adaptive Fuzzy Integral Sliding Mode Control for Flexible Air-Breathing Hypersonic Vehicles Subject to Input Nonlinearity

AbstractThis paper proposes a fuzzy integral sliding mode control strategy for flexible air-breathing hypersonic vehicles with input nonlinearity. Based on the complex nonlinear dynamics in the considered vehicles, a control-oriented model, which can retain the dominant features of the higher-fidelity model, is adopted for the control design. First, the T-S fuzzy approach is utilized to model the nonlinear dynamic of flexible air-breathing hypersonic vehicles, and the input nonlinearity model, which comprises dead-zones, sector nonlinearities, and actuator saturation, is considered. Then, based on the constructed T-S fuzzy model, a novel fuzzy integral sliding mode control method is proposed. This method can eliminate the reaching phase of the traditional sliding mode control by designing a novel sliding surface. Moreover, by the parallel-distributed compensation scheme, a sufficient condition is established to guarantee the global robust stability of the sliding mode dynamics in the specified surface in ...