Neutral Time-delay Systems Research Articles

Observers and State Reconstructions for Linear Neutral Time-Delay Systems

The problem of state reconstruction is discussed for linear neutral systems with a finite number of commensurable point delays. Using as models systems with coefficients in a ring and following a geometric point of view, feasible and constructing procedures are proposed for the construction of observers of increasing complexity. Conditions are given to characterize neutral systems with delays for which linear observers exist not depending on the derivatives of the state. Some examples illustrating the results are worked out in details.

Lyapunov matrices for neutral type time delay systems

In this paper two procedures for the computation of Lyapunov matrices of neutral type time delay systems are presented. The first one is a semi-analytic method, it consist in solving a two points boundary value problem for a delay free system. The second one is a piece-wise linear approximation of the Lyapunov matrix. An algorithm for the estimation of the error based on Lyapunov-Krasovskii functionals is also proposed. Copyright © 2007 IFAC.

Stabilization of Neutral Time-Delay Systems

This paper addresses the stabilization problem for neutral time-delay systems. Starting from a transfer approach, we develop a general algebraic framework for the study of the stabilization. The stability considered in this paper is the exponential one. We introduce a class of generalized operators, and we show the existence of a coprime factorization over this class. The main result of this paper concerns strictly proper systems that are not formally stable. It is shown that any stabilizing compensator, which is a real rational fraction in s and e −θs , is necessarily not proper. Copyright © 2007 IFAC

An EP algorithm for stability analysis of interval neutral delay-differential systems

As well-known, evolutionary programming (EP) algorithms have been considered as promising techniques for global optimal search. The main objective of this paper is to develop a novel EP algorithm for the robust stability analysis of interval neutral delay-differential systems. Two main results are obtained in this paper. First a delay-dependent criterion is derived for ensuring the stability of degenerate neutral time-delay systems, and then by solving some optimization problems, which will be defined later, the robust stability of interval neutral delay-differential systems can be guaranteed. Two numerical examples are given to illustrate the results.

Quadratic stability and stabilization of switched dynamic systems with uncommensurate internal point delays

This paper deals with the quadratic stability and linear state-feedback and output-feedback stabilization of switched delayed linear dynamic systems with, in general, a finite number of non-commensurate constant internal point delays. The results are obtained based on Lyapunov’s stability analysis via appropriate Krasovsky–Lyapunov’s functionals and the related stability study is performed to obtain both delay independent and delay dependent results. It is proved that the stabilizing switching rule is arbitrary if all the switched subsystems are quadratically stable and that it exists a (in general, non-unique) stabilizing switching law when the system is polytopic, stable at some interior point of the polytope but with non-necessarily stable parameterizations at the vertices defining the subsystems. It is also proved that two subsystems individually parametrized in different polytopic-type sets which are not quadratically stable might be stabilized by a (in general, non-unique) switching law provided that a convexity-type condition is fulfilled at each existing pair of vertices, one corresponding to each subsystem. Some extensions are provided for a typical class of neutral time-delay systems.

Global exponential stability conditions for generalized state-space systems with time-varying delays

A unified approach is proposed to deal with the exponential stability for generalized state-space systems with time-varying delays. Many systems models can be regarded as special cases of the considered systems; such as neutral time-delay systems and delayed cellular neural networks. Delay-dependent stability criteria are proposed to guarantee the global exponential stability for generalized state-space systems with two cases of uncertainties. Two numerical examples are given to show the effectiveness of our method.

Delay-dependent H-infinity filtering for neutral time-delay systems

This paper deals with the robust delay-dependent H-infinity filtering problem for neutral delay differential systems. The resulting filter is of the Luenberger observer type, and it guarantees that the filtering systems remains asymptotically stable and satisfies a prescribed H-infinity performance level. The Lyapunov stability theory and the descriptor model transformation are used for analysis of the system and are expected to be least conservative as compared with existing design methods. Some examples are provided to demonstrate the validity of proposed design approach.

Stability of Linear Neutral Time-Delay Systems: Exact Conditions via Matrix Pencil Solutions

In this note, we study the stability properties of linear neutral delay systems. We consider systems described by both neutral differential-difference and state-space equations, and we seek to determine the delay margin of such systems, that is, the largest range of delay values for which a neutral delay system may preserve its stability. In both cases, we show that the delay margin can be found by computing the eigenvalues and generalized eigenvalues of certain constant matrices, which can be executed efficiently and with high precision. The results extend previously known work on retarded systems, and demonstrate that similar stability tests exist for neutral systems; in particular, the tests require essentially the same amount of computation required for retarded systems.

An optimal linear-quadratic digital tracker for analog neutral time-delay systems

In this paper, an optimal hybrid tracking control problem for continuous neutral time-delay systems is formulated and studied. An optimal linear integral quadratic cost function that has a high-gain property is used for tracking control specification. Two interpolation methods are applied to directly convert the original analog neutral time-delay system into an equivalent digital retarded time-delay system, and meanwhile convert the continuous-time quadratic cost function into a discretized form. Then, an extended state vector is constructed for an associate extended discrete-time optimal control problem without time delay. Using the standard discrete-time linear-quadratic optimal control theory and an indirect digital redesign technique with a predictive feature, an effective digital tracker is designed for the original analog neutral time-delay system. An example is finally given for illustrating the effectiveness of the new tracker design method.

LYAPUNOV MATRICES FOR A CLASS OF NEUTRAL TYPE TIME DELAY SYSTEMS

A class of neutral type time delay systems is presented for which computation of Lyapunov matrices is reduced to solution of an auxiliary two point boundary problem for a delay free system of matrix equations.

H∞ OUTPUT FEEDBACK CONTROL FOR UNCERTAIN NEUTRAL TIME-DELAY SYSTEMS:AUGMENTED DYNAMICS AND AUGMENTED LYAPUNOV FUNCTIONAL APPROACHES

In this paper the robust H∞ output feedback control of uncertain neutral time-delay systems with norm-bounded type uncertainties is investigated. The control input is utilized as the augmenting state term and the system is represented in augmented dynamics form which enables to handle the design of the H∞ output feedback controller in terms of convex linear matrix inequalities (LMI) form which can be solved via interior-point algorithms. A novel augmented Lyapunov-Krasovskii functional is selected to obtain sufficient LMI conditions for the existence of delay-dependent H∞ output feedback control. Any model transformation and bounding for cross terms are strictly avoided to overcome the conservativeness of the results. A delay-dependent bounded real lemma is also presented in LMI form. Finally, several numerical examples are given to illustrate the effectiveness of the proposed method.

Exponential estimates for neutral time delay systems with multiple delays

AbstractExponential estimates and sufficient conditions for the exponential stability of linear neutral time delay for systems with multiple delays are given. The case of systems with uncertainties, including uncertainties in the difference operator, is considered. The proofs follows from new results on non‐homogeneous difference equations evolving in continuous time combined with the Lyapunov–Krasovskii functionals approach. The conditions are expressed in terms of linear matrix inequalities. The particular case of neutral time delay systems with commensurate delays, which leads to less restrictive exponential estimates, is also addressed. Copyright © 2005 John Wiley & Sons, Ltd.

H∞ Observer-Based Control for a Class of Uncertain Neutral Time-Delay Systems via LMI Optimization Approach

In this paper, the H∞ observer-based control for a class of uncertain neutral time-delay systems is considered. The linear matrix inequality (LMI) optimization approach is used to design the H∞ robust control with disturbance attenuation. Two classes of observer-based controls are proposed and their H∞-norm bounds are given. The control and observer gains are given from the LMI feasible solutions. A numerical example is given to illustrate the results.

Lyapunov functionals and Lyapunov matrices for neutral type time delay systems: a single delay case

Quadratic Lyapunov functionals with a given time derivative for the case of neutral type time delay systems have been presented in Rodriguez et al. (“Robust stability of neutral systems: a Lyapunov–Krasovskii constructive approach”, International Journal of Robust and Nonlinear Control, 14, pp. 1345–1358, 2004). In this contribution a new form of the functionals is proposed. The functionals now do not include the time derivative of the system state. This modification provides new quadratic bounds for the functionals and makes them useful in computation of exponential estimates for solutions of the systems, as well as in calculation of the robustness bounds. Special attention has also been paid to the Lyapunov matrices which define the functionals. A new definition of the matrices is given, and their properties are analysed in detail.

Guaranteed Cost Observer–Based Controls for a Class of Uncertain Neutral Time-Delay Systems

In this paper, guaranteed-cost observer-based controls for a class of uncertain neutral time-delay systems are considered. The asymptotic stabilization for the uncertain neutral systems is guaranteed with an observer-based feedback control. The linear matrix inequality (LMI) approach is used to design the observer-based feedback control system. Two classes of observer-based controls are proposed and their guaranteed costs are given. The control and observer gains are given from the LMI feasible solutions. A convex optimization problem with LMIs is formulated to design the optimal guaranteed-cost observer-based controls which minimize the guaranteed cost of the system considered. A numerical example is given to illustrate the results.

Exponential estimates for neutral time-delay systems: an LMI approach

Exponential estimates and sufficient conditions for the exponential stability of linear neutral time delay systems are given. The estimates are obtained for the case of known parameters as well as the uncertain case, including uncertainties in the difference term. The proof is based on Lyapunov-Krasovskii functionals, and the conditions are expressed in terms of linear matrix inequalities (LMIs).

中立型むだ時間システムのＬＭＩ型安定条件―特性方程式からのアプローチ

In this paper, exponential stability for neutral time-delay systems is discussed. First a sufficient condition is driven by using the characteristic equation, which is corresponding to the small gain theorem in the input-output stability theory. Based on this condition, an LMI stability condition is given by estimating the bound of L∞ norm of the time-delay element using the Padé approximants. The condition can also be applied to retarded time-delay systems in a special case. Numerical examples illustrate that when the time-delay is relatively short the obtained condition is less conservative than previous LMI ones led from the Lyapunov stability theory.

Robust stability of neutral systems: a Lyapunov‐Krasovskii constructive approach

AbstractIn this paper, robust stability of uncertain linear neutral systems is analysed via a Lyapunov–Krasovskii constructive approach. This paper is the first attempt to compute the Lyapunov–Krasovskii functional for a given time derivative functional w(·) for the class of linear neutral type time delay systems. Copyright © 2004 John Wiley & Sons, Ltd.

The Cluster Treatment of Characteristic Roots and the Neutral Type Time-Delayed Systems

A new methodology is presented for assessing the stability posture of a general class of linear time-invariant—neutral time-delayed systems (LTI-NTDS). It is based on a “Cluster Treatment of Characteristic Roots CTCR” paradigm, which yields a procedure called the Direct Method (DM). The technique offers a number of unique features: It returns exact bounds of time delay for stability, as well as the number of unstable characteristic roots of the system in an explicit and nonsequentially evaluated function of time delay. As a direct consequence of the latter feature, the new methodology creates entirely, all existing stability intervals of delay, τ. It is shown that the Direct Method inherently enforces an intriguing necessary condition for τ-stabilizability, which is the main contribution of this paper. This, so-called, “small delay” effect, was recognized earlier for NTDS, only through some cumbersome mathematics. Furthermore, the Direct Method is also unique in handling systems with unstable starting posture for τ=0, which may be τ-stabilized for higher values of delay. Example cases are provided.

Delay-dependent stability criterion for neutral time-delay systems via linear matrix inequality approach

In this paper, the asymptotic stability problem for a class of neutral systems with discrete and distributed delays is considered. Based on linear matrix inequality, a delay-dependent criterion is proposed to guarantee asymptotic stability for such systems. Some numerical examples are given to illustrate our main result.