Improved robust stability criteria for uncertain linear neutral‐type systems via novel Lyapunov‐Krasovskii functional

The stability problem for the uncertain time‐varying delayed neutral‐type system is concerned in this paper. By introducing a novel Lyapunov‐Krasovskii functional (LKF) related to a delay‐product‐type function and two delay‐dependent matrices, some new delay‐dependent robust stability sufficient conditions are derived, which are based on convex linear matrix inequality (LMI) framework. The sufficient conditions in this paper can reduce the conservativeness of some recent previous ones. In the end, some numerical examples, including a linear neutral‐type system, the partial element equivalent circuit and a general linear system, show the effectiveness of the proposed method.     

Improved Robust Stability Criteria for Time‐Delay Lur'e System

This paper deals with the problem of the robustly absolute stability for neutral‐type Lur'e systems with mixed time‐varying delay. By combining the piecewise analysis theory with the reciprocally convex method and Wirtinger‐based inequality technology, some new delay‐dependent stability criteria are proposed via a modified Lyapunov‐Krasovskii functional (LKF) approach. The stability conditions can be solved by using standard linear matrix inequality (LMI) convex optimization solvers. The criteria are less conservative than some previous ones. Three numerical examples are presented to show the effectiveness of the proposed approach.     

Further results on delay‐dependent robust stability conditions of uncertain neutral systems

This paper deals with the problem of robust stability analysis for uncertain neutral systems. In terms of a linear matrix inequality (LMI), an improved delay‐dependent asymptotic stability criterion is developed without using bounding techniques on the related cross product terms. Based on this, a new delay‐dependent LMI condition for robust stability is obtained. Numerical examples are provided to show that the proposed results significantly improve the allowed upper bounds of the delay size over some existing ones in the literature. Copyright © 2005 John Wiley & Sons, Ltd.     

Delay‐Dependent Robust Stability Criteria For Uncertain Neutral Systems With Mixed Time‐Varying Discrete And Neutral Delays

In this paper, a new class of augmented quasi full size Lypunov‐Krasovskii functional is introduced for the robust stability of uncertain neutral systems with mixed time‐varying discrete and neutral delays. The nonlinear parameter perturbations and norm‐bounded uncertainties are taken into consideration separately. Delay‐dependent robust stability criteria are derived in the form of linear matrix inequalities. Numerical examples are presented to illustrate the significant improvement on the conservativeness of the delay bound over some reported results in the literature.     

Robust stabilizers for an implicit dynamical delay system of the neutral type

A feedback stabilization problem is investigated for a class of imperfectly known implicit systems with discrete and distributed delays. The imperfections acting on the systems, which may be time‐, state‐, delayed state‐, and/or input‐dependent, are modelled as additive nonlinear perturbations influencing a known set of nonlinear functional differential equations of the neutral type. Sufficient conditions, which include a delay‐dependent matrix inequality and a delay‐dependent stability criterion involving some bounding parameters for the uncertainty in the system, are presented and a class of robust feedback stabilizers, including both memoryless and those with memory, are designed to guarantee a prescribed stability property for the class of implicit systems. Copyright © 2005 John Wiley & Sons, Ltd.     

ON ROBUST STABILITY OF LINEAR NEUTRAL SYSTEMS WITH MIXED DELAYS AND NORM‐BOUNDED UNCERTAINTY

This paper investigates the robust stability of linear neutral systems with mixed delays and norm‐bounded uncertainty. Using new Lyapunov‐Krasovskii functionals, less conservative delay‐dependent robust stability conditions for such systems in terms of linear matrix inequalities (LMIs) are derived. Numerical examples show that the results obtained in this paper significantly improve the estimate of the stability limit over some existing results in other literature.     

A New Delay‐Dependent Stability Criterion For Neutral Delay‐Differential Systems

This paper investigates the problem of asymptotic stability for neutral delay‐differential systems. Using the Lyapunov method, we derive a new delay‐dependent sufficient condition for the stability of systems in terms of the linear matrix inequality (LMI). Numerical examples show that the results obtained in this paper significantly improve the estimate of stability limit over some existing results reported previously in the literature.     

Delay‐dependent stability and stabilization of neutral time‐delay systems

This paper is concerned with the problem of stability and stabilization of neutral time‐delay systems. A new delay‐dependent stability condition is derived in terms of linear matrix inequality by constructing a new Lyapunov functional and using some integral inequalities without introducing any free‐weighting matrices. On the basis of the obtained stability condition, a stabilizing method is also proposed. Using an iterative algorithm, the state feedback controller can be obtained. Numerical examples illustrate that the proposed methods are effective and lead to less conservative results. Copyright © 2008 John Wiley & Sons, Ltd.     

Robust absolute stability for general neutral type Lurie indirect control systems

This note concerns the robust absolute stability analysis for a class of general neutral type Lurie indirect control systems with nonlinearity located in an infinite sector or finite one. By using Lyapunov functional of quadratic form with integral term and introducing some free‐weighting matrices, some delay‐dependent robust absolute stability criteria are presented in terms of strict linear matrix inequalities. Neither model transformation nor bounding technique is required here. The obtained criteria are less conservative than previous ones, which are illustrated by numerical examples. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

STABILITY ANALYSIS OF UNCERTAIN DISCRETE‐TIME SYSTEMS WITH TIME‐VARYING STATE DELAY: A PARAMETER‐DEPENDENT LYAPUNOV FUNCTION APPROACH

This paper presents several new robust stability conditions for linear discrete‐time systems with polytopic parameter uncertainties and time‐varying delay in the state. These stability criteria, derived by defining parameter‐dependent Lyapunov functions, are not only dependent on the maximum and minimum delay bounds, but also dependent on uncertain parameters in the sense that different Lyapunov functions are used for the entire uncertainty domain. It is established, theoretically, that these robust stability criteria for the nominal and constant‐delay case encompass some existing result as their special case. The delay‐dependent and parameter‐dependent nature of these results guarantees the proposed robust stability criteria to be potentially less conservative.     

An analysis of the exponential stability of linear stochastic neutral delay systems

This paper is concerned with the analysis of the mean square exponential stability and the almost sure exponential stability of linear stochastic neutral delay systems. A general stability result on the mean square and almost sure exponential stability of such systems is established. Based on this stability result, the delay partitioning technique is adopted to obtain a delay‐dependent stability condition in terms of linear matrix inequalities (LMIs). In obtaining these LMIs, some basic rules of the Ito calculus are also utilized to introduce slack matrices so as to further reduce conservatism. Some numerical examples borrowed from the literature are used to show that, as the number of the partitioning intervals increases, the allowable delay determined by the proposed LMI condition approaches h_max, the maximal allowable delay for the stability of the considered system, indicating the effectiveness of the proposed stability analysis. Copyright © 2013 John Wiley & Sons, Ltd.     

A delay decomposition approach to delay‐dependent stability for linear systems with time‐varying delays

This paper is concerned with delay‐dependent stability for linear systems with time‐varying delays. By decomposing the delay interval into multiple equidistant subintervals, on which different Lyapunov functionals are chosen, and new Lyapunov‐Krasvskii functionals are then constructed. Employing these new Lyapunov‐Krasvskii functionals, some new delay‐dependent stability criteria are established. The numerical examples show that the obtained results are less conservative than some existing ones in the literature. Copyright © 2009 John Wiley & Sons, Ltd.     

Delay‐dependent robust stability and stabilization of uncertain neutral systems

This 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     

Improved robust stability criteria for uncertain systems with time‐varying delay

This paper is concerned with the delay‐dependent stability and robust stability for uncertain systems with time‐varying delay. Through constructing an appropriate type of Lyapunov‐Krasovskii functional and proving its positive definiteness, using slack matrices and a convex combination condition, the delay‐dependent stability criteria, which are less conservative, are derived in terms of linear matrix inequalities. Numerical examples are also given to illustrate the improvement on the conservatism of the delay bound over some existing results. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Delay‐dependent robust stability analysis for switched time‐delay systems with polytopic uncertainties

In this paper, sufficient conditions are provided for the stability of switched retarded and neutral time‐delay systems with polytopic‐type uncertainties. It is assumed that the delay in the system dynamics is time‐varying and bounded. Parameter‐dependent Lyapunov functionals are employed to obtain criteria for the exponential stability of the system in the form of linear matrix inequality (LMI). Free‐weighting matrices are then provided to express the relationship between the system variables and the terms in the Leibniz–Newton formula. Numerical examples are presented to show the effectiveness of the results. Copyright © 2014 John Wiley & Sons, Ltd.     

Augmented Lyapunov functional and delay‐dependent stability criteria for neutral systems

In this paper, an augmented Lyapunov functional is proposed to investigate the asymptotic stability of neutral systems. Two methods with or without decoupling the Lyapunov matrices and system matrices are developed and shown to be equivalent to each other. The resulting delay‐dependent stability criteria are less conservative than the existing ones owing to the augmented Lyapunov functional and the introduction of free‐weighting matrices. The delay‐independent criteria are obtained as an easy corollary. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods. Copyright © 2005 John Wiley & Sons, Ltd.     

A less conservative robust stability criteria for uncertain neutral systems with mixed delays

This paper is concerned with the problem of the delay-dependent robust stability of neutral systems with mixed delays and time-varying structured uncertainties. By considering the cross-terms with additional design parameters, a complete form of Lyapunov–Krasovskii functional is constructed. Then some free weighting matrices are introduced, and a sufficient stability condition is obtained in terms of linear matrix inequalities. The obtained criterion is dependent on the sizes of neutral delay and discrete delay and are less conservative than those produced by previous approaches. Numerical examples are given to illustrate both the improvement the proposed method provides over some existing ones and the relationship between the neutral- and discrete-delay.     

Delay‐range‐dependent robust stability and stabilization for uncertain systems with time‐varying delay

This paper concerns delay‐range‐dependent robust stability and stabilization for time‐delay system with linear fractional form uncertainty. The time delay is assumed to be a time‐varying continuous function belonging to a given range. On the basis of a novel Lyapunov–Krasovskii functional, which includes the information of the range, delay‐range‐dependent stability criteria are established in terms of linear matrix inequality. It is shown that the new criteria can provide less conservative results than some existing ones. Moreover, the stability criteria are also used to design the stabilizing state‐feedback controllers. Numerical examples are given to demonstrate the applicability of the proposed approach. Copyright © 2007 John Wiley & Sons, Ltd.     

Delay‐dependent criteria for general decay synchronization of discontinuous fuzzy neutral‐type neural networks with time‐varying delays

This paper aims to investigate the general decay synchronization analysis of discontinuous fuzzy neutral‐type neural networks. Under the framework of Filippov solutions, based on functional differential inclusions theory, inequality technique and by constructing a modified delay‐dependent Lyapunov‐Krasovskii functional, some new delay‐dependent criteria are provided to guarantee the general decay synchronization via the effective nonlinear feedback controller. The neural network model considered is more generalized, some previous fuzzy neural networks can be regard as the special cases. Moreover, some recent results on the delay‐independent criteria ensuring the general decay synchronization can also be extended and concluded. These can be seen from the given corollaries and remarks which are provided to make the comparisons and show the advantages. Finally, some numerical examples and simulations are provided to illustrate the correctness.     

Delay‐dependent stability of nonlinear hybrid neutral stochastic differential equations with multiple delays

In this article, we study the delay‐dependent stability of a class of hybrid neutral stochastic differential equations (NSDEs) with multiple delays which is highly nonlinear. Some novel stability criteria are investigated according to Lyapunov functions and generalized Itô's formula. In particular, we generalize and improve the results in Shen et al, Systems & Control Letters (2018) from a single delay to multiple delays.