Improved results on robust stability of neutral systems with mixed time-varying delays and nonlinear perturbations

This paper considers the problem of robust stability of neutral systems with mixed time-varying delays and nonlinear perturbations. Two type uncertainties such as nonlinear time-varying parameter perturbations and norm-bounded uncertainties have been discussed. Based on the new Lyapunov–Krasovskii functional with triple integral terms, some integral inequalities and convex combination technique, a new delay-dependent stability criterion for the system is established in terms of linear matrix inequalities (LMIs). Finally, four numerical examples are given to illustrate the effectiveness and an improvement over some existing results in the literature with the proposed results.     

Further results on robust stability of neutral system with mixed time-varying delays and nonlinear perturbations

This paper studies delay-dependent robust stability problem for neutral system with mixed time-varying delays. The uncertainties under consideration are nonlinear time-varying parameter perturbations and norm-bounded uncertainties, respectively. Based on Lyapunov functional approach and linear matrix inequality technology, some improved delay-dependent stability conditions are derived by introducing free-weighting matrices. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.     

Robust stability criteria for a class of uncertain discrete-time systems with time-varying delay

In this paper, we consider the problem of delay-dependent robust stability of a class of uncertain discrete-time systems with time-varying delay using Lyapunov functional approach. Two categories of time-varying uncertainties are considered for the robust stability analysis: viz., (i) nonlinear perturbations and (ii) norm-bounded uncertainties. In the proposed stability analysis, by exploiting a candidate Lyapunov functional, and using minimal number of slack matrix variables, less conservative stability criteria are developed in terms of linear matrix inequalities (LMIs) for computing the maximum allowable bound of the delay-range, within which, the uncertain system under consideration remains asymptotically stable in the sense of Lyapunov. The effectiveness of the proposed stability criteria is demonstrated using standard numerical examples.     

Robust stability and stabilization methods for a class of nonlinear discrete-time delay systems

This paper establishes new robust delay-dependent stability and stabilization methods for a class of nonlinear discrete-time systems with time-varying delays. The parameter uncertainties are convex-bounded and the unknown nonlinearities are time-varying perturbations satisfying Lipschitz conditions in the state and delayed-state. An appropriate Lyapunov functional is constructed to exhibit the delay-dependent dynamics and compensate for the enlarged time-span. The developed methods for stability and stabilization eliminate the need for over bounding and utilize smaller number of LMI decision variables. New and less conservative solutions to the stability and stabilization problems of nonlinear discrete-time system are provided in terms of feasibility-testing of new parametrized linear matrix inequalities (LMIs). Robust feedback stabilization methods are provided based on state-measurements and by using observer-based output feedback so as to guarantee that the corresponding closed-loop system enjoys the delay-dependent robust stability with an L₂ gain smaller that a prescribed constant level. All the developed results are expressed in terms of convex optimization over LMIs and tested on representative examples.     

Robust stability criteria for systems with interval time-varying delay and nonlinear perturbations

This paper considers the robust stability for a class of linear systems with interval time-varying delay and nonlinear perturbations. A Lyapunov-Krasovskii functional, which takes the range information of the time-varying delay into account, is proposed to analyze the stability. A new approach is introduced for estimating the upper bound on the time derivative of the Lyapunov-Krasovskii functional. On the basis of the estimation and by utilizing free-weighting matrices, new delay-range-dependent stability criteria are established in terms of linear matrix inequalities (LMIs). Numerical examples are given to show the effectiveness of the proposed approach.     

Exponential Stability for Time-Delay Systems with Interval Time-Varying Delays and Nonlinear Perturbations

In this paper, the problem of an exponential stability for time-delay systems with interval time-varying delays and nonlinear perturbations is investigated. Based on the Lyapunov method, a new delay-dependent criterion for exponential stability is established in terms of LMI (linear matrix inequalities). Numerical examples are carried out to support the effectiveness of our results.     

Delay Range-Dependent Stability Analysis for Markovian Jumping Stochastic Systems with Nonlinear Perturbations

This article addresses the problem of delay-dependent stability for Markovian jumping stochastic systems with interval time-varying delays and nonlinear perturbations. The delay is assumed to be time-varying and belongs to a given interval. By resorting to Lyapunov–Krasovskii functionals and stochastic stability theory, a new delay interval-dependent stability criterion for the system is obtained. It is shown that the addressed problem can be solved if a set of linear matrix inequalities (LMIs) are feasible. Finally, a numerical example is employed to illustrate the effectiveness and less conservativeness of the developed techniques.     

Robust Stability Criteria for Uncertain Neutral Systems with Interval Time-Varying Delay

In this paper, we consider the problem of robust stability of a class of linear uncertain neutral systems with interval time-varying delay under (i) nonlinear perturbations in state, and (ii) time-varying parametric uncertainties using Lyapunov-Krasovskii approach. By constructing a candidate Lyapunov-Krasovskii (LK) functional, that takes into account the delay-range information appropriately, less conservative robust stability criteria are proposed in terms of linear matrix inequalities (LMI) to compute the maximum allowable bound for the delay-range within which the uncertain neutral system under consideration remains asymptotically stable. The reduction in conservatism of the proposed stability criterion over recently reported results is attributed to the fact that time-derivative of the LK functional is bounded tightly without neglecting any useful terms using a minimal number of slack matrix variables. The analysis, subsequently, yields a stability condition in convex LMI framework, that can be solved non-conservatively at boundary conditions using standard LMI solvers. The effectiveness of the proposed stability criterion is demonstrated through standard numerical examples.     

Sufficient Conditions for Robust Stability of LQG Optimal Control Systems Including Delayed Perturbations

Linear-quadratic Gaussian (LQG) optimal control systems subject to time-varying delay and nonlinear state perturbations are considered. Some robust stability conditions are derived which result in several bounds on the delayed state perturbations so that the uncertain linear-quadratic Gaussian optimal control systems with time-varying delay can remain stable in the sense of uniform ultimate boundedness. The modified Lyapunov equation and the improved Razumikhin-type theorem are employed to investigate such robust stability conditions. Finally, a numerical example is given to demonstrate the validity of the results.     

New delay-dependent robust stability criterion for uncertain neutral systems with time-varying delay and nonlinear uncertainties

This paper investigates the robust stability of uncertain neutral system with time-varying delay and nonlinear uncertainties. By using Lyapunov method and linear matrix inequality technology, a new delay-dependent stability criteria is obtained and formulated in terms of linear matrix inequalities (LMIs) which can be easy to check the robust stability of the considered systems. Numerical examples are given to indicate significant improvements over some existing results.     

On robustly exponential stability of uncertain neutral systems with time-varying delays and nonlinear perturbations

The issue of robustly exponential stability for uncertain neutral-type systems is considered in this paper. The uncertainties are nonlinear and the delays are time-varying. In terms of a linear matrix inequality (LMI), the new sufficient stability condition with delay dependence is presented. The model transformation and bounding techniques for cross terms are avoided based on an integral inequality. Two illustrative examples are proposed to show the effectiveness of our method.     

Switching design for exponential stability of a class of nonlinear hybrid time-delay systems

This paper addresses the exponential stability for a class of nonlinear hybrid time-delay systems. The system to be considered is autonomous and the state delay is time-varying. Using the Lyapunov functional approach combined with the Newton–Leibniz formula, neither restriction on the derivative of time-delay function nor bound restriction on nonlinear perturbations is required to design a switching rule for the exponential stability of nonlinear switched systems with time-varying delays. The delay-dependent stability conditions are presented in terms of the solution of algebraic Riccati equations, which allows computing simultaneously the two bounds that characterize the stability rate of the solution. A simple procedure for constructing the switching rule is also presented.     

具有非线性扰动的线性多时变时滞系统的鲁棒稳定性

采用了一类新型积分等式,研究了具有非线性扰动的线性多时变时滞系统的时滞相关鲁棒稳定性问题,并推广得到一般的时滞相关－时滞变化率无关的鲁棒稳定性条件.数值实例表明,稳定性条件的保守性也有所减少.     

Optimization Approach to the Robustness of Linear Delay Systems

By using the Lyapunov equation approach and an improved Razumikhin-type theorem, this paper presents a new robust stability criterion for a linear system subject to delayed time-varying nonlinear perturbations. Then, by using a parameter optimization technique, an efficient algorithm is derived for determining a desirable matrix for the Lyapunov equation. As a consequence, less conservative robust stability bounds for the perturbed system are achieved. Numerical examples are included to demonstrate the effectiveness of the proposed approach.     

Novel robust stability criteria for uncertain stochastic Hopfield neural networks with time-varying delays

The problem of stochastic robust stability of a class of stochastic Hopfield neural networks with time-varying delays and parameter uncertainties is investigated in this paper. The parameter uncertainties are time-varying and norm-bounded. The time-delay factors are unknown and time-varying with known bounds. Based on Lyapunov–Krasovskii functional and stochastic analysis approaches, some new stability criteria are presented in terms of linear matrix inequalities (LMIs) to guarantee the delayed neural network to be robustly stochastically asymptotically stable in the mean square for all admissible uncertainties. Numerical examples are given to illustrate the effectiveness and less conservativeness of the developed techniques.     

Adaptive stabilization of uncertain unified chaotic systems with nonlinear input

This paper addresses the problem of adaptive stabilization of uncertain unified chaotic systems with nonlinear input in the sector form. A novel representation of nonlinear input function, that is, a linear input with bounded time-varying coefficient, is firstly established. Then, an adaptive control scheme is proposed based on the new nonlinear input model. By using Barbalat’s lemma, the asymptotic stability of the closed-loop system is proved in spite of system uncertainties, external disturbance and input nonlinearity. One of the advantages of the proposed design method is that the prior knowledge on the plant parameter, the bound parameters of the uncertainties and the slope parameters inside the sector nonlinearity is not required. Finally, numerical simulations are performed to verify the analytical results.     

Stability of perturbed switched nonlinear systems with delays

This paper addresses the stability problems of perturbed switched nonlinear systems with time-varying delays. It is assumed that the nominal switched nonlinear system (perturbation-free system) is uniformly exponentially stable and that the perturbations satisfy a linear growth bound condition. It is revealed that there exists an upper bound of perturbation guaranteeing that the perturbed system preserves the stability property of the nominal system, locally or globally, depending on both perturbations and the nominal system itself. An example is provided to illustrate the proposed theoretical results.     

一类非线性时滞网络控制系统的无源性分析

本文研究了一类非线性时滞网络控制系统的无源性问题.利用Lyapunov稳定性理论,结合线性矩阵不等式(LMI)技术,通过构造Lyapunov-Krasovskii泛函,在考虑两种不同时滞的情况下,获得了系统满足无源性的充分条件,最后通过仿真算例验证了结论的正确性和方法的有效性.     

Stability analysis for a class of functional differential equations and applications

The problem of Lyapunov stability for functional differential equations in Hilbert spaces is studied. The system to be considered is non-autonomous and the delay is time-varying. Known results on this problem are based on the Gronwall inequality yielding relative conservative bounds on nonlinear perturbations. In this paper, using more general Lyapunov-Krasovskii functional, neither model variable transformation nor bounding restriction on nonlinear perturbations is required to obtain improved conditions for the global exponential stability of the system. The conditions given in terms of the solution of standard Riccati differential equations allow to compute simultaneously the two bounds that characterize the stability rate of the solution. The proposed method can be easily applied to some control problems of nonlinear non-autonomous control time-delay systems.