Stability Of Uncertain Neutral Systems Research Articles

Event-triggered Quantized Stabilization for Uncertain Neutral Systems

Event-triggered Quantized Stabilization for Uncertain Neutral Systems

Further results on robust stability for uncertain neutral systems with distributed delay

This paper studies the problem of robust stability for uncertain neutral systems with distributed delay. By utilizing the incorporation of a new integral inequality technique and a novel Lyapunov–Krasovskii functional, some reduced conservative delay-dependent stability conditions for asymptotic stability are established. Then some special cases of neutral systems are discussed. Based on these delay-dependent stability conditions, the condition for robustness is obtained for uncertain linear delayed systems. All these stability conditions are given in terms of linear matrix inequalities (LMIs), which can easily be computed by the LMI toolbox of Matlab. Finally, several examples are discussed in detail to display the usefulness and superiority of the obtained results.

On robust stability for uncertain neutral systems with non-differentiable interval time-varying discrete delay and nonlinear perturbations

In this paper, we investigate the problem of delay-range-dependent robust stability analysis for uncertain neutral systems with interval time-varying delays and nonlinear perturbations. The restriction on the derivative of the discrete interval time-varying delay is removed. By applying the augmented Lyapunov–Krasovskii functional approach, new improved integral inequalities, descriptor model transformation, Leibniz–Newton formula and utilization of zero equation, new delay-range-dependent robust stability criteria are derived in terms of linear matrix inequalities (LMIs) for the considered systems. Numerical examples have shown to illustrate the significant improvement on the conservatism of the delay upper bound over some reported results.

DELAY-DECOMPOSITION APPROACH FOR THE ROBUST STABILITY OF UNCERTAIN NEUTRAL SYSTEMS WITH DISTRIBUTED DELAYS

This paper deals with the problem of robust stability of uncertain neutral systems with distributed delays.A new delay-dependent stability condition is derived by using the delay-decomposition approach.Firstly,by non-uniformly dividing the delay interval into N segments,a new appropriate Lyapunov-Krasovskii(L-K) functional for each segment is constructed.Then,with the integral inequality approach,a new delay-dependent stability condition is formulated in terms of linear matrix inequalities.The proposed approach involves neither model transformation nor freeweighting matrix,so the complexity is reduced both in theory and in computation.Numerical examples show that the proposed method enlarge the more conservative upper bound for the delay-range.

Exponential Stability Criteria for Neutral System with Mixed Time-Varying Delays and Nonlinear Perturbations

This paper focuses on the issue of robustly exponential stability for uncertain neutral systems with mixed time-varying delays and nonlinear perturbations. Some new sufficient conditions dependent on the delays are derived in terms of Lyapunov-Krasovskii functionals combined with free-weighting matrices. Two numerical examples are given to show the effectiveness of the proposed method.

Robust Exponential Stability for Uncertain Neutral Systems with Interval Time-Varying Delay and Nonlinear Perturbations

In this paper, the robust exponential stability problem is investigated for a class of neutral systems with interval time-varying delay and nonlinear perturbations. Based on the Lyapunov-Krasovskii functionals in conjunction with Leibniz-Newton formula, novel LMI-based delay-dependent and delay-independent criteria are proposed to guarantee the robust exponential stability with a convergence rate for our considered systems. Finally, numerical examples are illustrated to show the improved results from using the proposed method.

An improved delay-dependent criterion for stability of uncertain neutral systems with mixed time delays

This paper addresses the asymptotic stability problem for a class of uncertain neutral systems with discrete and distributed time delays. By considering a new Lyapunov functional involving discrete-delay interval into two equal parts and employing the linear matrix inequality technique together with free weighting matrix approach, less conservative stability criteria are derived to compute the maximum allowable upper bound for the delay-range within which the considered uncertain neutral system is asymptotically stable. The obtained stability conditions are formulated in terms of linear matrix inequalities (LMIs) that can be easily solved by using the MATLABLMI toolbox package. The effectiveness of the proposed stability criterion is demonstrated through a numerical example and the results are compared with some existing works to show the less conservatism of the obtained results.

New augmented Lyapunov functional method for stability of uncertain neutral systems with equivalent delays

This paper is concerned with the delay-dependent stability for neutral systems with equivalent delays and norm-bounded uncertainties. Through constructing a new augmented LKF and proving its positive definiteness, introducing some slack matrices and using integral inequality, the improved delay-dependent stability criteria are derived in terms of linear matrix inequalities, and it is theoretically established that obtained results are less conservative than some existing stability conditions. Finally, numerical examples are given to illustrate the significant improvement on the conservatism of the delay bound over some existing results.

Robust stability and control for uncertain neutral time delay systems

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 Robust Exponential Stability Criterion for Uncertain Neutral Systems with Discrete and Distributed Time‐Varying Delays and Nonlinear Perturbations

We investigate the problem of robust exponential stability for uncertain neutral systems with discrete and distributed time‐varying delays and nonlinear perturbations. Based on the combination of descriptor model transformation, decomposition technique of coefficient matrix, and utilization of zero equation and new Lyapunov functional, sufficient conditions for robust exponential stability are obtained and formulated in terms of linear matrix inequalities (LMIs). The new stability conditions are less conservative and more general than some existing results.

Delay and its time-derivative dependent robust stability of uncertain neutral systems with saturating actuators

This note concerns the problem of the robust stability of uncertain neutral systems with time-varying delay and saturating actuators. The system considered is continuous in time with norm bounded parametric uncertainties. By incorporating the free weighing matrix approach developed recently, some new delay-dependent stability conditions in terms of linear matrix inequalities (LMIs) with some tuning parameters are obtained. An estimate of the domain of attraction of the closed-loop system under a priori designed controller is proposed. The approach is based on a polytopic description of the actuator saturation nonlinearities and the Lyapunov-Krasovskii method. Numerical examples are used to demonstrate the effectiveness of the proposed design method.

Augmented Lyapunov functional approach for stability of neutral systems with mixed delays

This paper is concerned with the neutral-delay-dependent and discrete-delay-dependent stability for uncertain neutral systems with mixed delays and norm-bounded uncertainties. Through constructing a new augmented Lyapunov-Krasovskii functional and proving its positive definiteness, introducing some slack matrices and using integral inequality, the improved delay-dependent stability criteria are derived in terms of linear matrix inequalities. Numerical examples are given to illustrate the significant improvement on the conservatism of the delay bound over some existing results. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Delay Dependent Robust Exponential Stability Criterion for Perturbed and Uncertain Neutral Systems with Time Varying Delays

This paper deals with the issue of robust exponential stability of uncertain neutral system with time varying delay and nonlinear perturbations. Using Lyapunov-Krasovskii functional, new sufficient delay dependent stability conditions have been derived in terms of Linear Matrix Inequalities LMIs solved using efficient convex optimization algorithms. Neither model transformation, nor estimating techniques for cross terms, nor free weighting matrices are involved in this work. Numerical examples are considered to show the efficiency of the proposed stability approach.

Improved Asymptotic Stability Criteria for Uncertain Neutral Systems with Time-varying Discrete Delays

Abstract—This paper investigates the robust stability of uncertain neutral system with time-varying delay. By using Lyapunov method and linear matrix inequality technology, new delay-dependent stability criteria are 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.

Robust stability for uncertain neutral systems with mixed time-varying delays

The robust stability of uncertain neutral systems with mixed time-varying delays is investigated in this paper. The uncertainties under consideration are norm-bounded and time-varying. Based on the Lyapunov stability theory, a delay-dependent stability criterion is derived and given in the form of a linear matrix inequality (LMI). Finally, a numerical example is given to illustrate significant improvement over some existing results.

Exponential stability for uncertain neutral systems with Markov jumps

This paper deals with the global exponential stability problems for stochastic neutral Markov jump systems (MJSs) with uncertain parameters and multiple time-delays. The delays are respectively considered as constant and time varying cases, and the uncertainties are assumed to be norm bounded. By selecting appropriate Lyapunov-Krasovskii functions, it gives the sufficient condition such that the uncertain neutral MJSs are globally exponentially stochastically stable for all admissible uncertainties. The stability criteria are formulated in the form of linear matrix inequalities (LMIs), which can be easily checked in practice. Finally, two numerical examples are exploited to illustrate the effectiveness of the developed techniques.

Augmented Lyapunov functional approach to stability of uncertain neutral systems with time-varying delays

In this paper, the problem of delay-dependent stability for uncertain neutral systems with time-varying delays is considered. The parameter uncertainties are assumed to be norm-bounded. By constructing an augmented Lyapunov functionals, a novel delay-dependent stability criterion for the system is established in terms of LMIs (linear matrix inequalities). Six numerical examples are given to show the effectiveness of proposed method.

On delay-dependent robust stability of uncertain neutral systems with interval time-varying delays

In this paper, the problem of a new delay-dependent robust stability criterion for neutral systems is investigated. The considered system has time-varying structured uncertainties and interval time-varying delays. Based on the Lyapunov method, a delay-dependent criterion for asymptotic stability is established in terms of LMI (linear matrix inequality). Numerical examples are carried out to support the effectiveness of our results.

Delay‐dependent robust stability and stabilization of uncertain neutral systems

AbstractThis paper discusses the problems of the delay‐dependent robust stability and stabilization of uncertain neutral systems with time‐varying delays. Delay‐dependent stability criteria are derived by taking the relationships between the terms in the Leibniz‐Newton formula into account. Free‐weighting matrices are employed to express these relationships, and they are easy to obtain because the new criteria are based on linear matrix inequalities. Moreover, the stability criteria are extended to the design of a stabilizing state feedback controller. Numerical examples demonstrate that these criteria are effective and are an improvement on previous ones. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

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.