Neutral Time-delay Systems Research Articles

Formula omitted] filter design for a class of neutral stochastic time delay systems

This paper is devoted to the problem of L2–L∞ filtering for a class of neutral stochastic systems with different neutral time-delay, discrete delay and distributed delays. By constructing a new Lyapunov–Krasovskii functional, some novel delay-dependent mean-square exponential stability criteria are obtained in terms of linear matrix inequalities. In the derivation process, neither model transformation method nor free-weighting matrix approach is used. Based on the obtained stability criterion, sufficient condition for the existence of the full-order L2–L∞ filter is given by introducing two appropriate slack matrix variables. Desired L2–L∞ filter is designed such that the resulting filtering error system is mean-square exponential stable and a prescribed L2–L∞ disturbance attenuation level is satisfied. Finally, numerical examples are included to illustrate the effectiveness and the benefits of the proposed method.

Stabilization of decentralized descriptor-type neutral time-delay systems by time-delay controllers

Stabilization of non-impulsive descriptor-type linear time-invariant (LTI) neutral time-delay systems by decentralized feedback is considered. It is shown that, provided that the stability axis is to the right of the finite-spectrum abscissa of the system, there exists a stabilizing decentralized finite-dimensional LTI or a decentralized descriptor-type LTI neutral time-delay controller for such a system if and only if the system does not have any unstable decentralized fixed modes.

Mobile robots in singular time-delay form – Modeling and control

Modeling and control of a mobile robotic manipulator having a wheeled platform, with passive and active suspension, and a manipulator carrying an inertia load, is studied. The overall model is developed in a nonlinear singular neutral time delay system form. The special case of flat road and single joint manipulator is studied and the linear approximant of its model is derived. Using a dynamic controller involving delays, I/O decoupling between the vertical position of the load and the velocity of the wheeled platform under the constraint of norm bounded load contact forces, is derived.

Parametric Investigation of Thermoacoustic Instability (TAI) in a Rijke Tube: A Time-Delay Perspective

This paper presents a novel deployment of a recent mathematical paradigm for predicting the thermo-acoustic instability (TAI) of a Rijke tube in the relevant parametric space. This benchmark problem in combustion science has been studied for over 1½ centuries with phenomenal achievements both in theoretical and practical fronts. The new paradigm is called the Cluster Treatment of Characteristic Roots (CTCR), which is originally developed to assess the asymptotic stability of Linear Time Invariant (LTI) Time-delayed Systems (TDS). A notorious subcategory within LTI-TDS is called “Neutral TDS”, which matches the characteristics of the linearized dynamics of thermo-acoustic instability. The CTCR is shown to reveal a non-conservative and exhaustive linear stability map of the Rijke tube within the space of its geometric and operational parameters. We present a review of this paradigm as well as several case studies to demonstrate its capabilities and some encouraging comparison with the earlier literature. This paper is a concept document and it is prepared with the intent of providing a breeding ground for studies beyond its present coverage.

Stability Analysis of Time-Varying Neutral Time-Delay Systems

We propose a new technique of stability analysis for a general family of linear time-varying systems with delay of neutral type. We establish results of exponential stability through a new technique which relies on the notion of nonnegative system and the design of linear time-varying Lyapunov functionals. However, the studied systems are not assumed to be nonnegative.

ROBUST CONTROLLER DESIGN FOR NEUTRAL TIME-DELAY SYSTEMS

A robustness measure that accounts for the uncertainties in a neutral time-delay system is defined. Using this measure, a robust controller design approach, which is based on a nominal model, is proposed. The proposed approach guarantees robust stability once a condition depending on the robustness measure is satisfied. An example is also presented to demonstrate the proposed approach.

Thermo-acoustic instability: Theory and experiments

This article deals with thermo-acoustic instability (TAI) on a simple Rijke tube, an extensively studied combustion test platform. We revisit the mathematical model of the dynamics and show that when linearized it falls into the class of linear time-invariant neutral time delay systems. In order to analyze its stability characteristics, we implement a recent mathematical paradigm called the cluster treatment of characteristic roots (CTCR). It can reveal the stable operating regions in the space of the operational parameters, such as the geometric dimensions of the Rijke tube. The results of this prediction mechanism are very favorably compared with experimental findings.

RobustH∞Control of Neutral System with Time-Delay for Dynamic Positioning Ships

Due to the input time-delay existing in most thrust systems of the ships, the robustH∞controller is designed for the ship dynamic positioning (DP) system with time-delay. The input delay system is turned to a neutral time-delay system by a state-derivative control law. The less conservative result is derived for the neutral system with state-derivative feedback by the delay-decomposition approach and linear matrix inequality (LMI). Finally, the numerical simulations demonstrate the asymptotic stability and robustness of the controller and verify that the designed DP controller is effective in the varying environment disturbances of wind, waves, and ocean currents.

Stabilization of neutral time-delay systems with actuator saturation via auxiliary time-delay feedback

This paper investigates the stabilization problem for neutral time-delay systems with actuator saturation. Different from the existing techniques, the auxiliary time-delay feedback is introduced for the first time in this paper. Based on such a technique, the saturation nonlinearity is represented as the convex combination of state feedback and auxiliary time-delay feedback. By employing free-weighting matrix technique and Jensen integral inequalities, and performing the accurate estimation of the lower bounds of L–K functionals, the improved delay-dependent local stabilization conditions are proposed in terms of linear matrix inequalities (LMIs). Numerical examples illustrate the reduced conservatism of the proposed conditions in this paper.

On robustness of predictor feedback control of linear systems with input delays

This paper is concerned with the robustness of the predictor feedback control of linear systems with input delays. By applying certain equivalent transformations on the characteristic equation associated with the closed-loop system, we first transform the robustness problem of a predictor feedback control system into the stability problem of a neutral time-delay system containing an integral operator in the derivative. The range of the allowable input delay for this neutral time-delay system can be computed by exploring its delay dependent stability conditions. In particular, delay dependent stability conditions for the neutral time-delay system are established by partitioning the delay into segments. The conservatism of this method can be reduced when the number of segments in the partition is increased. Numerical examples are worked out to illustrate the effectiveness of the proposed method.

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

Summary 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.

Improved Stability Criteria for Linear Neutral Time‐Delay Systems

AbstractThis paper is concerned with the problem of stability analysis of linear neutral time delay systems. First, a new simple Lyapunov‐Krasovskii functional is constructed based on delay partitioning approach, then, a novel improved delay‐dependent stability criterion is established to guarantee the asymptotic stability of the neutral system. The obtained stability criterion is expressed in terms of linear matrix inequalities, which can be verified easily by means of standard software. Numerical examples are given to illustrate the effectiveness of the proposed method and the advantage over some existing results.

Robust Exponential Stabilization Results for Impulsive Neutral Time-Delay Systems with Sector-Bounded Nonlinearity

In this paper, the problem of robust exponential stabilization analysis for nonlinear neutral systems with time-varying delays under impulsive control is addressed. Sufficient delay-dependent exponential stabilization results are derived in terms of linear matrix inequalities by constructing suitable Lyapunov---Krasovskii functional. The control gain matrices are designed using impulsive state-feedback control approach. Also, the nonlinear function is assumed to satisfy the sector-bounded condition which includes Lipschitz condition as a special case. Further numerical examples are provided to show the effectiveness of the derived results.

Robust PID Stabilization of Linear Neutral Time-Delay Systems

This paper deals with the problem of robust stabilization of neutral timedelay systems using proportional-Integral-Derivative (PID) controller. A graphical approach which will obtain the set of robust stabilizing PID controllers is presented. The main point in this approach is the frequency response of the neutral system, which can effectively reduce the mathematical complexities of system modeling. It is shown that our the proposed method is effective and useful for many of real control systems deal with time-delays and parametric uncertainties. It is illustrated by an example at the end.

Controllability of a class of nonlinear neutral time-delay systems

In this paper, the problem of controllability for a class of time-varying nonlinear neutral time-delay systems is considered. Sufficient conditions based on Krasnoselskii’s fixed point theorem are derived for the system to be globally and locally controllable. Eventually, some illustrative examples are given in order to present the results established.

Finite-Time Stability of Neutral Fractional Time-Delay Systems via Generalized Gronwalls Inequality

This paper studies the finite-time stability of neutral fractional time-delay systems. With the generalized Gronwall inequality, sufficient conditions of the finite-time stability are obtained for the particular class of neutral fractional time-delay systems.

Practical stability and stabilization of a class of nonlinear neutral type time delay systems with multiple delays: BMI’s approaches

In this paper, the practical stability and stabilization of a class of nonlinear neutral type time delay systems with multiple delays and bounded perturbations is discussed. Sufficient conditions based on Lyapunov-Krasovskii functionals are derived. They are formulated in terms of the feasibility of a set of Bilinear Matrix Inequalities (BMI’s). A practical exponential estimate of the system response is also obtained. This approach is shown to be useful in the solution of an engineering problem: the elimination of the stick-slip phenomenon in the drilling process.

Critical frequencies and parameters for linear delay systems: A Lyapunov matrix approach

A new method, based on recent results concerning the construction of the Lyapunov matrix of delay systems, reveals conditions under which the characteristic function has a root s0 such that −s0 is also a root. As the pure imaginary roots, which are crucial in the stability analysis of time delay systems, are of that type, this method gives rise to a novel approach for the delay independent and delay dependent stability analyses of systems with delay that are multiple of a basic delay, distributed delays and of a class of neutral type time delay systems. A number of examples are given to illustrate the approach and to show its strength.

Robust delay-dependent feedforward control of neutral time-delay systems via dynamic IQCs

This paper studies the design problem of delay-dependent based robust and optimal feedforward controller design for a class of time-delay control systems having state, control and neutral type delays which are subject to norm-bounded uncertainties and type measurable or observable disturbance signals. Two independent loops which include state-feedback and dynamic feedforward controller form the basis of the proposed control scheme in this study. State-feedback controller is generally used in stabilisation of the nominal delay-free system, whereas the feedforward controller is used for improving disturbance attenuation performance of the overall system. In order to obtain less conservative results, the delay and parametric uncertainty effects are treated in operator view point and represented by frequency-dependent (dynamic) integral quadratic constraints (IQCs). Moreover, sufficient delay-dependent criterion is developed in terms of linear matrix inequalities (LMIs) such that the time-delay system having parametric uncertainties is guaranteed to be asymptotically stable with minimum achievable disturbance attenuation level. Plenty of numerical examples are provided at the end, in order to illustrate the efficiency of the proposed technique. The achieved results on minimum achievable disturbance attenuation level and maximum allowable delay bounds are exhibited to be less conservative in comparison to those of controllers having only feedback loop.

Computation of Unstable Characteristic Roots of Neutral Delay Systems

We present an algorithm based on the argument principle for computing all unstable characteristic roots of a class of neutral time delay systems. By consecutively subdividing a bounded rectangular or half circular region on the right half complex plane into smaller ones, initial approximate positions of all unstable roots can be located efficiently. With these approximate positions as starting points for Newton's method, approximations for all roots are refined iteratively. The performance of the algorithm is shown by an example.