Stability Of Neutral Delay-differential Systems Research Articles

Delay-dependent stability analysis for uncertain neutral systems with time-varying delays

This paper investigates the stability of neutral delay-differential systems with mixed multiple time-varying delay arguments. Based on the Lyapunov functional method, and the relationship between the system states and the derivatives of these states, we present a new asymptotical stability criterion and a new robust stability criterion in terms of only one simple linear matrix inequality (LMI), which guarantees stability for such systems with time-varying delays. This LMI can be easily solved by various convex optimization algorithms. Two examples are given to illustrate the advantages of the proposed methods over the existing ones.

Some new simple stability criteria of linear neutral systems with a single delay

This article mainly considers the linear neutral delay-differential systems with a single delay. Using the characteristic equation of the system, new simple delay-independent asymptotic and exponential stability criteria are derived in terms of the matrix measure, the spectral norm and the spectral radius of the corresponding matrices. Numerical examples demonstrate that our criteria are less conservative than those of previous corresponding results [L.M. Li, Stability of linear neutral delay-differential systems, Bull. Aust. Math. Soc. 38 (1988) 339–344; G.D. Hu, G.D. Hu. Some simple criteria for stability of neutral delay-differential systems, Appl. Math. Comput. 80 (1996) 257–271; D.Q. Cao, Ping He, Sufficient conditions for stability of linear neutral systems with a single delay, Appl. Math. Lett. 17 (2004) 139–144; G.D. Hu, G.D. Hu, B. Cahlon, Algebraic criteria for stability of linear neutral systems with a single delay, J. Comput. Appl. Math. 135 (2001) 125–130].

Some sufficient conditions for exponential stability of linear neutral functional differential equations

Abstract In this paper, we give some sufficient conditions for exponential stability of linear neutral functional differential equations. The obtained results are extensions of the recent results in [D.Q. Cao, P. He, Stability criteria of linear neutral systems with a single delay, Appl. Math. Comput. 148 (2004) 135–143, D.Q. Cao, P. He, Sufficient conditions for stability of linear neutral systems with a single delay, Appl. Math. Lett. 17 (2004) 139–144], [G.-D. Hu, G.-D. Hu, X.F. Zou, Stability of linear neutral systems with multiple delays: boundary criteria, Appl. Math. Comput. 148 (2004) 707–715; J.H. Park, S. Won, A note on stability of neutral delay-differential systems, J. Franklin Inst. 336 (1999) 1–9] to linear neutral functional differential equations.

Simple algebraic criteria for stability of neutral delay-differential systems

The asymptotic stability of linear neutral systems with a single delay is investigated in this article. Based on the characteristic equation, new algebraic criteria for the stability of the system are derived in terms of the spectral radius of corresponding modulus matrices. The significance of our new criteria is that it takes into consideration the structure information of the system matrices, thus reducing the conservatism found in the literature. Numerical examples are given to demonstrate the new stability criteria and to compare them with the previous results in the literature.

Stability of neutral delay-differential systems with nonlinear perturbations

In this paper, the problem of the stability analysis for neutral delay-differential systems with nonlinear perturbations is investigated. Using the Lyapunov method, we present new sufficient conditions for the stability, in terms of the linear matrix inequality (LMI), which can be easily solved by various convex optimization algorithms. Numerical examples are given to illustrate the application of the proposed method.

A note on stability of neutral delay-differential systems

In this note, asymptotic stability of linear neutral delay-differential systems is investigated. A delay-independent sufficient condition for the stability of the system is derived in terms of the spectral radius. The proposed criterion requires more relaxed assumption than those reported in the literature. The effectiveness of the method is illustrated in numerical examples.

Stability of neutral delay-differential systems: Boundary criteria

This paper deals with the delay-dependent stability of linear-invariant neutral delay-differential systems with a positive constant delay. Six criteria that are described by evaluating a corresponding harmonic function on the boundary of a certain rectangular region are presented.

Some simple criteria for stability of neutral delay-differential systems

This paper deals with the stability of linear neutral delay-differential systems. Some simple criteria for delay-independent stability of this class of problems which are described by evaluating the measure and norm of corresponding matrices are presented. The main results proposed in this study are sharper than those reported in the literature.