Class Of Linear Neutral Systems Research Articles

Asymptotic properties of neutral type linear systems

Exponential stability and solution estimates are investigated for a delay systemx˙(t)−A(t)x˙(g(t))=∑k=1mBk(t)x(hk(t)) of a neutral type, where A and Bk are n×n bounded matrix functions, and g,hk are delayed arguments. Stability tests are applicable to a wide class of linear neutral systems with time-varying coefficients and delays. In addition, explicit exponential estimates for solutions of both homogeneous and non-homogeneous neutral systems are obtained for the first time. These inequalities are not just asymptotic estimates, they are valid on every finite segment and evaluate both short- and long-term behavior of solutions.

Stability Analysis of a Class of Neutral Type Systems in a Critical Case Without Restriction on the Principal Neutral Term

AbstractThis study focuses mainly on the stability of a class of linear neutral systems in a critical case, that is, where the spectral radius of the principal neutral term (matrix H in this paper) is equal to 1. It is difficult to determine the stability of such systems via existing methods. In this study, a sufficient stability criterion for the critical case without restrictions on the principal neutral term is given in terms of the existence of solutions to a linear matrix inequality.

Robustness analysis for a class of linear neutral systems in a critical case

This study pays attention to robust stability of a class of uncertain neutral systems in a critical case, where the spectral radius of the principal neutral term (matrix H in this study) is equal to 1. It is shown that usual methods cannot deal with such systems with uncertainties. Thus, a novel method is developed, whose idea is to examine whether or not an existing stability criterion still holds when the uncertainties are sufficiently small. More specifically, it is to examine whether or not the existing stability criterion in terms of a linear matrix inequality (LMI) still has a solution with the sufficiently small uncertainties. By analysing the structure of the solution, a new robust stability criterion is derived in terms of the existence of solutions to an equation. An application shows the effectiveness of the proposed method by dealing with a problem caused by numerical methods when solving LMIs.

Linear matrix inequality approach for stability analysis of linear neutral systems in a critical case

This study mainly focuses on the stability of a class of linear neutral systems in a critical case, that is, the spectral radius of the principal neutral term (matrix H) is equal to 1. It is difficult to determine the stability of such systems by using existing methods. In this study, a sufficient stability criterion for the critical case is given in terms of the existence of solutions to a linear matrix inequality (LMI). Moreover, it is also shown that the proposed stability criterion conforms with a fact that the considered linear neutral systems are unstable when H has a Jordan block corresponding to the eigenvalue of modulus 1. An illustrative example is presented to determine the stability of a linear neutral system whose principal neutral term H has multiple eigenvalues of modulus 1 without Jordan chains. This is difficult in existing studies.

Delay-dependent Stability for Systems with Fast-varying Neutral-type Delays via a PTVD Compensation

Abstract The stability for a class of linear neutral systems with time-varying delays is studied in this paper, where delay in neutral-type term includes a fast-varying case (i.e., the derivative of delay is more than one), which has never been considered in current literature. The less conservative delay-dependent stability criteria for this system are proposed by applying new Lyapunov-Krasovskii functional and novel polynomials with time-varying delay (PTVD) compensation technique. The aim to deal with systems with fast-varying neutral-type delay can be achieved by using the new functional. The benefit brought by applying the PTVD compensation technique is that some useful elements can be included in criteria, which are generally ignored when estimating the upper bound of derivative of Lyapunov-Krasovskii functional. A numerical example is provided to verify the effectiveness of the proposed results.

Dynamic output feedback H ∞ control problem for a class of linear neutral systems

This note presents the solution of dynamic output feedback H ∞ control problem for a class of linear neutral systems in delay dependent case. First, sufficient conditions for the existence of such controllers is obtained by Lyapunov method in terms of linear matrix inequalities (LMIs). A parameterized characterization of the controllers is given in terms of feasible solutions to the certain matrix inequalities by using Matlab LMI Toolbox. Finally, a numerical example is given to illustrate the proposed 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.

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.

On delay-dependent stability for linear neutral systems

This paper focuses on the problem of uniform asymptotic stability of a class of linear neutral systems. Sufficient conditions for delay-dependent stability are given in terms of the existence of solutions of some linear matrix inequalities. Furthermore, the proposed technique extends to neutral systems the results obtained for delay-difference equations using model transformations. Illustrative examples are included.

On delay dependent stability for linear neutral systems

This paper focuses on the problem of uniform asymptotic stability of a class of linear neutral systems. The delays are assumed to be unknown, but constant. Sufficient conditions for delay-dependent stability are given in terms of the existence of symmetric and positive definite solutions of some linear matrix inequalities. Furthermore, the proposed technique extends the results obtained for delay-difference equations to neutral systems using model transformations. The derived results are illustrated by a numerical example.

On The Stability of a Class of Uncertain Linear Neutral Systems: An LMI Approach With Applications

This paper focuses on the problem of uniform asymptotic stability of a class of linear neutral systems including some time-varying and cone-bounded nonlinearities. The delay is assumed unknown, but constant. Sufficient conditions for delay-independent robust stability are given in terms of the existence of symmetric and positive definite solutions of some linear matrix inequalities. The proposed results are applied to the stability analysis of some classes of infinite-dimensional systems described by partial differential equations and which can be described in a neutral form.