Systems Of Neutral Type Research Articles

On stability criteria for uncertain delay-differential systems of neutral type with time-varying delays

In this paper, we propose a new stability criterion for uncertain neutral systems. The considered system has time-varying structured uncertainties and time-varying delay. Based on the Lyapunov method, a delay-dependent criterion for asymptotic stability is derived in terms of LMI (linear matrix inequality). Numerical examples are given to show the effectiveness of our results.

Stabilization of some fractional delay systems of neutral type

In this note, we give new stability tests which enable one to fully characterize the H ∞ -stability of systems with transfer function G ( s ) = r ( s ) p ( s ) + q ( s ) e - sh , where h > 0 and p , q , r are real polynomials in the variable s μ for 0 < μ < 1 . As an application of this, in the case r ( s ) = 1 and deg p = deg q = 1 , families of H ∞ -stabilizing controllers are given and a complete parametrization of all H ∞ -stabilizing controllers is obtained when | lim s ∈ C ⧹ R - | s | → ∞ p ( s ) / q ( s ) | > 1 .

Stability Analysis of PI TCP/AQM Networks: A Parameter Space Approach

This work focuses on deriving the necessary and sufficient stability condition of transmission control protocol (TCP) network with a proportional-integral (PI) active queue management (AQM) scheme via a parameter space approach. First, a fluid-flow TCP s nonlinear model is converted into a linear time-delay system of neutral type. Second, the stability of the closed-loop system is characterized in terms of the network's and the controller s parameters. By simulation studies we investigate the boundary s relations of these two kinds of parameters in the parameter space and illustrate how PI controller s parameters affect the stability. Finally, different stability conditions are compared to show the less conservatism of our necessary- and sufficient-condition-based method, and simulation experiments by both Matlab and NS-2 are conducted to prove our claim.

Robust absolute stability criteria for uncertain Lur'e systems of neutral type

AbstractThis paper is concerned with robust absolute stability of uncertain Lur'e systems of neutral type. Some delay‐dependent stability criteria are obtained and formulated in the form of linear matrix inequalities. The criteria cover some existing results as their special cases. Neither model transformation nor bounding technique for cross terms is involved through derivation of the stability criteria. Numerical examples show the effectiveness of the criteria. Copyright © 2007 John Wiley &amp; Sons, Ltd.

Stability analysis and H ∞ filtering for delay differential systems of neutral type

Stability analysis and H∞ filter design for linear neutral systems is discussed. First, a new Lyapunov–Krasovskii functional is constructed to derive a new less conservative delay-dependent stability condition. It is then shown that the introduction of more free matrices sometimes cannot help reduce the conservatism of the obtained conditions. This new criterion is applied to designing a suitable H∞ filter of the Luenberger observer type, and a new design scheme is formulated in terms of the feasibility of a linear matrix inequality. Finally, some examples are given to illustrate the effectiveness of the proposed approach.

On robustly exponential stability of uncertain neutral systems with time-varying delays and nonlinear perturbations

The issue of robustly exponential stability for uncertain neutral-type systems is considered in this paper. The uncertainties are nonlinear and the delays are time-varying. In terms of a linear matrix inequality (LMI), the new sufficient stability condition with delay dependence is presented. The model transformation and bounding techniques for cross terms are avoided based on an integral inequality. Two illustrative examples are proposed to show the effectiveness of our method.

The Analysis of Exact Controllability of Neutral-Type Systems by the Moment Problem Approach

The problem of exact null-controllability is considered for a wide class of linear neutral-type systems with distributed delay. The main tool of the analysis is the application of the moment problem approach and the theory of the basis property of exponential families. A complete characterization of this problem is given. The minimal time of controllability is specified. The results are based on the analysis of the Riesz basis property of eigenspaces of the neutral-type systems in Hilbert space.

A criterion of constructive identifiability and complete controllability of linear stationary systems of neutral type

For linear stationary systems of neutral type, parametric criteria of constructive indentifiability and complete controllability are proved and constructive methods for solving these problems are presented. This paper is a continuation of work [1], where constructive solutions to the problem of complete controllability and identifiability were given for the case of a characteristic quasi-polynomial of the delayed type and the corresponding literature was presented; therefore, the historical notes concerning the problems studied are omitted in this paper.

Descriptor discretized Lyapunov functional method: analysis and design

Stability and state-feedback stabilization of linear systems with uncertain coefficients and uncertain time-varying delays are considered. The system under consideration may be unstable without delay, but it becomes asymptotically stable for positive values of the delay. A new descriptor discretized Lyapunov-Krasovskii functional (LKF) method is introduced, which combines the application of the complete LKF and the discretization method of K. Gu with the descriptor model transformation. For the first time, the new method allows to apply the discretized LKF method to synthesis problems. Moreover, the analysis of systems with polytopic time-invariant uncertainties is less restrictive by the new discretized method. Sufficient conditions for robust stability and stabilization of uncertain neutral type systems are derived in terms of linear matrix inequalities (LMIs) via input-output approach to stability. Numerical examples illustrate the efficiency of the new method.

ON ROBUST STABILITY OF LINEAR NEUTRAL SYSTEMS WITH TIME-VARYING DELAYS

The application of direct Lyapunov method to stability of neutral systems with time-varying delays is usually encountered with the restrictive assumption on the function in the right side of the differential equation. This function is supposed to satisfy the Lipshitz condition with respect to the delayed state derivative with a constant less than 1. In the present paper we extend input-output approach to stability of neutral type systems with uncertain time-varying delays and norm-bounded uncertainties. This allows to avoid the assumption on the Lipshitsian constant. Sufficient stability criteria are derived in the frequency domain and in the time domain, where the descriptor discretized Lyapunov Krasovskii Functional (LKF) is applied. As a by-product, new necessary conditions for neutral-delay-independent/retarded-delay-dependent stability are obtained. The method can be easily extended to L2-gain analysis and can be applied to design problems.

Convex Optimization Approach to Dynamic Output Feedback Control for Delay Differential Systems of Neutral Type

In this paper, the design problem of the dynamic output feedback controller for the asymptotic stabilization of a class of linear delay differential systems of the neutral type is considered. A criterion for the existence of such controller is derived based on the matrix inequality approach combined with the Lyapunov method. A parametrized characterization of the controller is given in terms of the feasible solutions to certain matrix inequalities, which can be solved by various convex optimization algorithms. A numerical example is given to illustrate the proposed design method.

Identifiability and Controllability Problems for Linear Second-Order Autonomous Systems of Neutral Type

Identifiability and Controllability Problems for Linear Second-Order Autonomous Systems of Neutral Type

Oscillation of differential systems of neutral type

We study oscillatory properties of solutions of systems $$\left[ {y_1 \left( t \right) - a\left( t \right)y_1 \left( {g\left( t \right)} \right)} \right]^\prime = p_1 \left( t \right)y_2 \left( t \right),$$ $$y'_2 \left( t \right) = - p_2 \left( t \right)f\left( {y_1 \left( {h\left( t \right)} \right)} \right),\quad t \geqslant t_0 .$$ .

An eigenvalue based approach for the stabilization of linear time-delay systems of neutral type

An eigenvalue based approach for the stabilization of linear neutral functional differential equations is presented, which extends the recently developed continuous pole placement method for delay equations of retarded type. The approach consists of two steps. First the stability of the associated difference equation is determined and a procedure is applied to compute the supremum of the real parts of its characteristic roots, which corresponds to computing the radius of the essential spectrum of the solution operator of the neutral equation. No restrictions are made on the dimension of the system and the number of delays. Also the effect of small delay perturbations is explicitly taken into account. As a result of this first step the stabilization problem of the neutral equation is reduced to a problem involving only a finite number of characteristic roots. As a second step, stabilization is achieved by shifting the rightmost or unstable characteristic roots to the left half plane in a quasi-continuous way, by applying small changes to the controller parameters, and meanwhile monitoring other characteristic roots with a large real part. A numerical example is presented.

On a class of strongly stabilizable systems of neutral type

We consider the strong stabilizability problem for a delayed system of neutral type. For simplicity the case of one delay in state is studied. We separate a class of such systems and give a constructive solution of the problem in this case, without the derivative of the localized delayed state. Our results are based on an abstract theorem on the strong stabilizability of contractive systems in Hilbert space. An illustrating example is also given.

Simulation of a photosynthesis

It is observed the differential equations system. The stable periodic solutions of the differential equa­tions system of neutral type is constructed, which is based on the theory of bifurcations.

On Computing the Maximum Time-Delay Bound for Stability of Linear Neutral Systems

This note is concerned with the stability problem of linear delay-differential systems of neutral type. A discretized Lyapunov functional approach is developed. The resulting stability criterion is formulated in the form of a linear matrix inequality. For nominal systems, the analytical results can be approached with fine discretization. Numerical examples show significant improvement over approaches in the literature.

Stability analysis of neutral type systems in Hilbert space

The asymtoptic stability properties of neutral type systems are studied mainly in the critical case when the exponential stability is not possible. We consider an operator model of the system in Hilbert space and use recent results on the existence of a Riesz basis of invariant finite-dimensional subspaces in order to verify its dissipativity. The main results concern the conditions of asymptotic non-exponential stability. We show that the property of asymptotic stability is not determinated only by the spectrum of the system but essentially depends on the geometric spectral characteristic of its main neutral term. Moreover, we present an example of two systems of neutral type which have both the same spectrum in the open left-half plane and the main neutral term but one of them is asymptotically stable while the other is unstable.

H∞ and BIBO stabilization of delay systems of neutral type

Frequency-domain tests for the H ∞ and BIBO stability of large classes of delay systems of neutral type are derived. The results are applied to discuss the stabilizability of such systems by finite-dimensional controllers.

On new stability criterion for delay-differential systems of neutral type

In this paper, a novel stability criterion is presented for neutral differential systems. Based on the Lyapunov method, the stability criterion is derived in terms of linear matrix inequalities which can be easily solved by efficient convex optimization algorithms. Numerical examples are included to show the effectiveness of the proposed method.