Improved stability criteria and controller design for linear neutral systems

This paper is concerned with the problems of stability and H∞ control of linear neutral systems. Firstly, some new simple Lyapunov-Krasovskii functionals are constructed by uniformly dividing the discrete delay interval into multiple segments, and choosing proper functionals with different weighted matrices corresponding to different segments in the Lyapunov-Krasovskii functionals. Then using these new simple Lyapunov-Krasovskii functionals, some new delay-dependent stability criteria are derived. These criteria include some existing results as their special cases and are much less conservative than some existing results, which is shown through a numerical example. Secondly, a delay-dependent bounded real lemma (BRL) is established. Employing the obtained BRL, some delay-dependent sufficient conditions for the existence of a delayed state feedback controller, which ensure asymptotic stability and a prescribed H∞ performance level of the corresponding closed-loop system, is formulated in terms of a linear matrix inequality (LMI). A numerical example is also given to illustrate the effectiveness of the design method

New delay-dependent synchronization criteria for Lur’e systems using time delay feedback control

This Letter is concerned with the problem of master–slave synchronization for Lur’e systems using time delay feedback control. Based on a more general Lur’e–Postnikov Lyapunov functional, some new delay-dependent synchronization criteria are obtained and formulated in the form of linear matrix inequalities (LMIs). These criteria cover some existing results as their special cases. In order to obtain less conservative results, no model transformation is involved through derivation of the synchronization criteria. An example shows that the result obtained in this Letter significantly improves some existing one

Stability of linear neutral systems with linear fractional norm-bounded uncertainty

This paper is concerned with the stability problem of uncertain linear neutral systems using a discretized Lyapunov functional approach. The uncertainty under consideration is linear fractional norm-bounded uncertainty which includes the routine norm-bounded uncertainty as a special case. A delay-dependent stability criterion is derived and is formulated in the form of linear matrix inequalities (LMIs). The criterion can be used to check the stability of linear neutral systems with both small and non-small delays. For nominal systems, the analytical results can be approached with fine discretization. For uncertainty systems with small delay, numerical examples show significant improvement over approaches in the literature. For uncertainty systems with non-small delay, the effect of the uncertainty on the maximum time-delay interval for asymptotic stability is also studied

Absolute stability of time-delay systems with sector-bounded nonlinearity

This paper deals with the problem of absolute stability of time-delay systems with sector-bounded nonlinearity. Some new delay-dependent stability criteria are obtained and formulated in the form of linear matrix inequalities (LMIs). Neither model transformation nor bounding technique for cross terms is involved through derivation of the stability criteria. Numerical examples show that the results obtained in this paper improve the estimate of the stability limit over some existing result

A new delay-dependent stability criterion for linear neutral systems with norm-bounded uncertainties in all system matrices

This paper deals with the problem of robust stability for a class of uncertain linear neutral systems. The uncertainties under consideration are of norm-bounded type and appear in all system matrices. A new delay-dependent stability criterion is obtained and formulated in the form of linear matrix inequalities (LMIs). Neither model transformation nor bounding technique for cross terms is involved through derivation of the stability criterion. Numerical examples show that the results obtained in this paper significantly improve the estimate of the stability limit over some existing results in the literature

On robust stability of neutral systems with time-varying discrete delay and norm-bounded uncertainy

This paper investigates the robust stability of uncertain linear neutral systems with time-varying discrete delay. A delay-dependent stability criterion is obtained and formulated in the form of a linear matrix inequality. Two numerical examples are given to indicate signi1cant improvements over some existing results

Robust stability for a class of linear systems with time-varying delay and nonlinear perturbations

The robust stability of uncertain linear systems with a single time-varying delay is investigated by employing a descriptor model transformation and a decomposition technique of the delay term matrix. The uncertainties under consideration are nonlinear perturbations and normbounded uncertainties, respectively. The proposed stability criteria are formulated in the form of a linear matrix inequality. Numerical examples are presented to indicate significant improvements over some existing results

On stability of linear neutral systems with mixed time delays : A discretized Lyapunov functional approach

This paper focuses on the stability problem for a class of linear neutral systems with mixed neutral and discrete delays. A discretized Lyapunov functional approach is developed for such kinds of systems. The resulting stability criteria are formulated in the form of a linear matrix inequality (LMI). These criteria are applicable to linear neutral systems with both small and non-small discrete delays. For nominal systems, the analytical results can be approached with fine discretization. For uncertain systems, the new approach is much less conservative. Numerical examples show significant improvement over approaches in the literature

A delay decomposition approach to stability and H∞ control of linear time-delay systems. Part II, H∞ control

This paper is concerned with H∞ control for linear time-delay systems. Delay-dependent bounded real lemmas (BRLs) are established by using a delay decomposition approach. Employing the obtained BRLs, some delay-dependent sufficient conditions for the existence of memoryless and delayed state feedback controllers, which ensure asymptotic stability and a prescribed H∞ performance level of the corresponding closedloop system, is formulated in terms of a linear matrix inequality (LMI). A practical example is given to illustrate the effectiveness of the design method

Stability criteria for a class of linear neutral systems with time-varying discrete and distributed delays

The robust stability of uncertain linear neutral systems with time-varying discrete and distributed delays is investigated by employing a descriptor model transformation and the decomposition technique of the discrete-delay term matrix. The proposed delay-dependent stability criteria are formulated in the form of a linear matrix inequality. Numerical examples are given to indicate significant improvements over some existing results