Robust Exponential Stability Analysis Research Articles

Robust exponential stability analysis of switched systems under switching boundary mismatch

AbstractSwitching boundary is an integral part of the switched system, but the existing literature on switched systems does not focus on the system under switching boundary mismatch. In this article, the switching boundary mismatch is considered, and the control strategy based on observation algorithm is designed for the state dependent switched system. By implementing the proposed strategy, the system can realize robust exponential stability and track the desired trajectory. Since the switching boundary mismatch is unmeasurable, an observation algorithm is designed. Combining the observation algorithm and iterative learning control law, the new control strategy can be derived. According to the Lyapunov stability theory and mode dependent average dwell time method, the robust exponential stability conditions of the closed‐loop system based on linear matrix inequalities are given. The mode dependent average dwell time of each subsystem can be solved simultaneously. Finally, simulations have been taken to verify the designed strategy can render the closed‐loop system achieve robust exponential stability and can track the desired trajectory.

Robust Exponential Stability Analysis of Switched Neural Networks with Interval Parameter Uncertainties and Time Delays

In this paper, the stability of switched neural networks (SNNs) with interval parameter uncertainties and time delays is investigated. First, the conditions for the existence and uniqueness of the equilibrium point of the system are discussed. Second, the average dwell time approach and M-matrix property are employed to obtain conditions to ensure the globally exponential stability of the delayed SNNs under constrained switching. Third, by resorting to inequality technique and the idea of vector Lyapunov function, sufficient condition to ensure the robust exponential stability of the delayed SNNs under arbitrary switching is derived. The form of the constructed Lyapunov functions is simple, which has certain commonality in studying delayed SNNs, and the proposed results not only are explicit but also reveal the relationship between the constrained switching and the arbitrary switching of the SNNs. Finally, two numerical examples are presented to illustrate the effectiveness and less conservativeness of the main results compared with the existing literature.

Nonlinear measure approach for the robust exponential stability analysis of interval inertial Cohen–Grossberg neural networks

This article is concerned with the existence and robust stability of an equilibrium point that related to interval inertial Cohen–Grossberg neural networks. Such condition requires the existence of an equilibrium point to a given system, so the existence and uniqueness of the equilibrium point are emerged via nonlinear measure method. Furthermore, with the help of Halanay inequality lemma, differential mean value theorem as well as inequality technique, several sufficient criteria are derived to ascertain the robust stability of the equilibrium point for the addressed system. The results obtained in this article will be shown to be new and they can be considered alternative results to previously results. Finally, the effectiveness and computational issues of the two models for the analysis are discussed by two examples. © 2016 Wiley Periodicals, Inc. Complexity 21: 459–469, 2016

New delay-range-dependent robust exponential stability criteria for uncertain linear systems with discrete interval and distributed time-varying delays and nonlinear perturbations

In this paper, we investigate the problem of robust exponential stability analysis for uncertain linear systems with discrete interval time-varying delay, distributed time-varying delay and nonlinear perturbations. Based on constructing an augmented Lyapunov–Krasovskii functional with some parameter, decomposition technique of coefficient matrix, mixed model transformation with Leibniz–Newton formula and utilization of zero equations, new delay-range-dependent robust exponential stability criteria are derived in terms of linear matrix inequalities (LMIs). Numerical examples are given to show the superiority of our results to those in the literature.

A Novel Approach to Robust Stability Analysis of Linear Time-Delay Systems

In this paper, we demonstrate that the Lyapunov-Krasovskii functional, which does not admit a quadratic lower bound, can be applied for the robust exponential stability analysis as well as for obtaining the exponential estimates for the solutions of linear time-invariant differential-difference systems with multiple delays.

New Delay-Range-Dependent Robust Exponential Stability Criteria of Uncertain Impulsive Switched Linear Systems with Mixed Interval Nondifferentiable Time-Varying Delays and Nonlinear Perturbations

We investigate the problem of robust exponential stability analysis for uncertain impulsive switched linear systems with time-varying delays and nonlinear perturbations. The time delays are continuous functions belonging to the given interval delays, which mean that the lower and upper bounds for the time-varying delays are available, but the delay functions are not necessary to be differentiable. The uncertainties under consideration are nonlinear time-varying parameter uncertainties and norm-bounded uncertainties, respectively. Based on the combination of mixed model transformation, Halanay inequality, utilization of zero equations, decomposition technique of coefficient matrices, and a common Lyapunov functional, new delay-range-dependent robust exponential stability criteria are established for the systems in terms of linear matrix inequalities (LMIs). A numerical example is presented to illustrate the effectiveness of the proposed method.

Robust exponential stability analysis for delayed neural networks with time-varying delay

Abstract This paper considers the problems of determining the robust exponential stability and estimating the exponential convergence rate for delayed neural networks with parametric uncertainties and time delay. The relationship among the time-varying delay, its upper bound, and their difference is taken into account. Theoretic analysis shows that our result includes a previous result derived in the literature. As illustrations, the results are applied to several concrete models studied in the literature, and a comparison of results is given.

Delay fractioning approach to robust exponential stability of fuzzy Cohen–Grossberg neural networks

In this paper, the problem of robust exponential stability analysis for a class of Takagi–Sugeno (TS) fuzzy Cohen–Grossberg neural networks with uncertainties and time-varying delays is investigated. A generalized activation function is used, and the assumptions such as boundedness, monotony and differentiability of the activation functions are removed. By using a Lyapunov–Krasovskii functional and employing the delay fractioning approach, a set of sufficient conditions are established for achieving the required result. The obtained conditions are proposed in terms of linear matrix inequalities (LMIs), so its feasibility can be checked easily via standard numerical toolboxs. The main advantage of the proposed criteria lies in its reduced conservatism which is mainly based on the time delay fractioning technique. In addition to that, a numerical example with simulation results is given to show the effectiveness of the obtained LMI conditions.

Robust Exponential Stability Analysis of Uncertain Discrete Time‐Varying Linear Systems

AbstractThis paper studies the robust exponential stability of uncertain discrete linear time‐varying (UDLTV) systems. The key tool is the recently proposed generating functions. It can be found that a class of improved generating functions (IGFS) can fully characterize the robust exponential stability of UDLTV systems, and the maximum exponential decay rate of system trajectories can be computed by the radius of convergence of the IGFS. Moreover, the application of convex optimization technique and dynamic programming method provides an effective algorithm for the computation of the IGFS. Finally, the numerical example illustrates the efficacy and advantage of the proposed approach.

Robust exponential stability analysis for interval Cohen–Grossberg type BAM neural networks with mixed time delays

In this paper, the robust exponential stability issue for the interval Cohen–Grossberg type BAM neural networks with nonsmooth behaved functions and mixed time delays is investigated. Firstly, based on Homomorphic mapping theory and nonsmooth analysis approach, the existence and uniqueness of the equilibrium point are proved. Secondly, by applying linear matrix inequality (LMI), free-weighting matrix technique, and available Lyapunov-Krasovskii functional method, some delay-dependent conditions are achieved in terms of LMIs to ensure the considered neural network to be globally robustly exponentially stable. The results obtained in this paper are little conservative compared with the previous results in the literature. Finally, two simulation examples are given to illustrate the validity of the theoretical results.

Exponential stability analysis for the switched stochastic Hopfield neural networks with time-varying delays

In this paper, the robust exponential stability analysis is investigated for a class of switched stochastic Hopfield neural systems with parameter uncertainties and stochastic perturbations. The parameter uncertainties are assumed to be norm bounded. Firstly, based on Lyapunov-Krasovskii functional and linear matrix inequality (LMI) tools, by means of multiple Lyapunov function techniques, a delay-dependent sufficient condition is derived for the switched stochastic neural networks with time-varying delays under an appropriate switching law. Secondly, the sufficient criteria are given to guarantee the uncertain switched stochastic Hopfield neural systems to be mean-square exponentially stable for all admissible parametric uncertainties. Finally, numerical examples are provided to illustrate the effectiveness of the proposed theory.

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.

Robust Exponential Stability Analysis for Interval Neural Networks with Time Delay

The problem of robust exponential stability analysis for nonlinear uncertain interval neural networks with time delay is investigated. The nonlinear uncertainties are assumed to satisfy the cone constraint conditions. The interval parameters of the neural networks are equivalent to norm matched parameter uncertainties via some matrix transformations. The stable criteria for the uncertain interval neural networks with time delays are developed by use of the Lyapunov stability theory. All the stability conditions in this paper are presented in terms of linear matrix inequalities.

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

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.

New global exponential stability criteria for interval-delayed neural networks

This paper is concerned with the problem of global robust exponential stability analysis for a class of interval cellular neural networks with time delay. By introducing a novel Lyapunov-Krasovslii function combined with the idea of delay fractioning, some delay-dependent conditions are derived in terms of the linear matrix inequality, which guarantee the considered interval delayed cellular neural networks to be globally exponentially stable. Moreover, the conservatism can be notably reduced as the fractioning becomes thinner. Some numerical examples are provided to demonstrate the advantages of the proposed results.

Robust exponential stability analysis of discrete-time switched Hopfield neural networks with time delay

The robust exponential stability problem in this paper for discrete-time switched Hopfield neural networks with time delay and uncertainty is considered. Firstly, the mathematical model of the system is established. Then by constructing a new Lyapunov–Krasovskii functional, some new delay-dependent criteria are developed, which guarantee the robust exponential stability of discrete-time switched Hopfield neural networks. A numerical example is provided to demonstrate the potential and effectiveness of the results obtained.

Robust stability analysis for uncertain stochastic neural networks with mixed time-varying delays

In this paper, the robust exponential stability analysis is investigated for a class of uncertain stochastic neural networks with discrete and distributed time-varying delays. Based on the Lyapunov functional method, and by applying the novel technique for estimating the upper bound of infinitesimal operator L of the stochastic process, the less conservative exponential stability criteria are derived in terms of Linear Matrix Inequalities (LMIs). Finally, two numerical examples are presented to show the less conservativeness of the obtained results.

Robust stability of stochastic Cohen–Grossberg neural networks with mixed time-varying delays

In the paper, the problem of robust exponential stability analysis is investigated for stochastic Cohen–Grossberg neural networks with both interval time-varying and distributed time-varying delays. By employing an augmented Lyapunov–Krasovskii functional, together with the LMI approach and definition on convex set, two delay-dependent conditions guaranteeing the robust exponential stability (in the mean square sense) of addressed system are presented. Additionally, the activation functions are of more general descriptions and the derivative of time-varying delay being less than 1 is released, which generalize and further improve those earlier methods. Numerical examples are provided to demonstrate the effectiveness of proposed stability conditions.

ROBUST EXPONENTIAL STABILITY OF STOCHASTIC TIME-DELAY SYSTEMS WITH UNCERTAINTIES AND NONLINEAR PERTURBATIONS

In this paper, the delay-dependent robust exponential mean-square stability analysis problem is considered for a class of uncertain stochastic systems with time-varying delay and nonlinear perturbations. Some sufficient conditions on delay-dependent robust exponential stability in the mean square are established in terms of linear matrix inequalities (LMIs) by exploiting a novel Lyapunov–Krasovskii functional and by making use of zero equations methods. These developed results indicate less conservatism than the existing ones due to the introduction of some free weighting matrices which can be selected properly. The new delay-dependent stability criteria are expressed as a set of LMIs, which can be readily solved by using standard numerical software. Numerical examples are provided to demonstrate the effectiveness and the applicability of the proposed criteria.

New results on robust exponential stability for discrete recurrent neural networks with time-varying delays

This paper is concerned with the problem of robust exponential stability analysis for uncertain discrete recurrent neural networks with time-varying delays. In terms of linear matrix inequality (LMI) approach, some novel stability conditions are proposed via a new Lyapunov function. Neither any model transformation nor free-weighting matrices are employed in our theoretical derivation. The established stability criteria significantly improve and simplify some existing stability conditions. Numerical examples are given to demonstrate the effectiveness of the proposed methods.