Stability Of Neutral Systems Research Articles

Lyapunov–Krasovskii characterization of the input-to-state stability for neutral systems in Hale’s form

The primary contribution of the paper is to show that the Lyapunov–Krasovskii conditions available in the literature, for checking the input-to-state stability property of systems described by neutral functional differential equations in Hale’s form, are also necessary. It is shown that the Lyapunov–Krasovskii conditions available in the literature are equivalent to the input-to-state stability property, for an enlarged class of neutral systems. Finally, a novel necessary and sufficient condition for the input-to-state stability property is provided.

Delay-Decomposition Stability Approach of Nonlinear Neutral Systems with Mixed Time-Varying Delays

This paper deals with the asymptotic stability of neutral systems with mixed time-varying delays and nonlinear perturbations. Based on the Lyapunov–Krasovskii functional including the triple integral terms and free weighting matrices approach, a novel delay-decomposition stability criterion is obtained. The main idea of the proposed method is to divide each delay interval into two equal segments. Then, the Lyapunov–Krasovskii functional is used to split the bounds of integral terms of each subinterval. In order to reduce the stability criterion conservatism, delay-dependent sufficient conditions are performed in terms of Linear Matrix Inequalities (LMIs) technique. Finally, numerical simulations are given to show the effectiveness of the proposed stability approach.

New Delay-dependent stability criteria for neutral systems with time-varying delay using delay-decomposition approach

This paper concerns with the problem of asymptotic stability for neutral systems with timevarying delays. With the introduction of delay-decomposition approach, some new delay-dependent stability criteria are established and formulated in the form of linear matrix inequalities. Both constant time delays and time-varying delays have been taken into account. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.

New exponential stability criteria for neutral system with time-varying delay and nonlinear perturbations

In this paper, the problem of exponential stability for neutral system with time-varying delay and nonlinear perturbations is investigated. By using the technology of model transformations, based on a linear matrix inequality (LMI) and a generalized Lyapunov-Krasovskii function, a new criterion for exponential stability with delay dependence is obtained. Due to a new integral inequality, the result is less conservative. Finally, some numerical examples are presented to illustrate the effectiveness of the method.

New augmented Lyapunov functional method for stability of uncertain neutral systems with equivalent delays

This paper is concerned with the delay-dependent stability for neutral systems with equivalent delays and norm-bounded uncertainties. Through constructing a new augmented LKF and proving its positive definiteness, introducing some slack matrices and using integral inequality, the improved delay-dependent stability criteria are derived in terms of linear matrix inequalities, and it is theoretically established that obtained results are less conservative than some existing stability conditions. Finally, numerical examples are given to illustrate the significant improvement on the conservatism of the delay bound over some existing results.

A Delay-Dividing Approach for Stability of Neutral System with Mixed Delays

This paper studies the stability problem for the neutral system with mixed delays. By constructing a novel Lyapunov functional based on a delay-dividing approach, some delay-dependent stability criteria are derived to guarantee the stability of the neutral system. It is established theoretically that the criteria are less conservative than recent reported ones. Two numerical examples are demonstrated to illustrate the effectiveness of the proposed results.

Stabilization of Neutral Systems with Saturating Actuators

A method is proposed for stabilization, using static state feedback, of systems subject to time-varying delays in both the states and their derivatives (i.e., neutral systems), in the presence of saturating actuators. Delay-dependent conditions are given to determine stabilizing state-feedback controllers with large domain of attraction, expressed as linear matrix inequalities, readily implementable using available numerical tools and with tuning parameters that make possible to select the most adequate solution. These conditions are derived by using a Lyapunov-Krasovskii functional on the vertices of the polytopic description of the actuator saturations. Numerical examples demonstrate the effectiveness of the proposed technique.

On Stability of Neutral Systems with Time-Varying Delay

This paper investigates the delay-dependent robust stability of neutral systems with time-varying discrete delays and time-varying structured uncertainties. New delay-dependent stability criteria are obtained and formulated in the form of a linear matrix inequality. Since the criteria take the sizes of the neutral delay, discrete delay and derivative of discrete delay into account, they are less conservative than previous methods. Numerical example is given to indicate significant improvements over some existing results.

Stability of Neutral Systems with Commensurate Delays and Poles Asymptotic to the Imaginary Axis

This paper addresses the $H_\infty$-stability analysis of neutral time-delay systems with multiple commensurate delays, including those with poles asymptotic to the imaginary axis. The location of asymptotic poles is completely described, and easy-to-check necessary and sufficient conditions of $H_\infty$-stability are derived. Robustness relative to a change in the delay or the parameters is discussed. Moreover, $H_\infty$-stabilizability by rational controllers is considered, and, finally, several examples are given.

Improved exponential stability criteria for uncertain neutral system with nonlinear parameter perturbations

This paper investigates the problem of robust exponential stability for neutral systems with time-varying delays and nonlinear perturbations. Based on a novel Lyapunov functional approach and linear matrix inequality technique, a new delay-dependent stability condition is derived. Since the model transformation and bounding techniques for cross terms are avoided, the criteria proposed in this paper are less conservative than some previous approaches by using the free-weighting matrices. One numerical example is presented to illustrate the effectiveness of the proposed results.

Augmented Lyapunov functional approach for stability of neutral systems with mixed delays

This paper is concerned with the neutral-delay-dependent and discrete-delay-dependent stability for uncertain neutral systems with mixed delays and norm-bounded uncertainties. Through constructing a new augmented Lyapunov-Krasovskii functional and proving its positive definiteness, introducing some slack matrices and using integral inequality, the improved delay-dependent stability criteria are derived in terms of linear matrix inequalities. Numerical examples are given to illustrate the significant improvement on the conservatism of the delay bound over some existing results. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

New stability analysis for linear neutral system via state matrix decomposition

This paper deals with the problem of delay-dependent stability for neutral systems. The matrix decomposition technique is employed to reduce the conservativeness of stability conditions. The main results are extended to the neutral system with time-varying uncertainties. The proposed methods are with simpler form in terms of LMI and better performance than the existing ones in the literatures. Numerical examples are given to illustrate the effectiveness of the proposed methods.

Robust stability of neutral systems: A discretized Lyapunov functional method

This paper focuses on the robust stability for time-delay systems of neutral type. A new complete Lyapunov-Krasovskii function (LKF) is developed. Based on this function and discretization, stability conditions in terms of linear matrix inequalities are obtained. A class of time-varying uncertainty of system matrices can be studied by the method.

Stability analysis of neutral systems with mixed delays

The stability of neutral systems with mixed delays is studied in this paper. A new discretized Lyapunov functional method is proposed. The method in this paper is less conservative than the existing ones and the results are very close to the analytical results. In addition, this method allows the coefficient matrix of the neutral term to have time-varying uncertainties.

Stability analysis of neutral systems with distributed delays

The stability of neutral systems with distributed delays is investigated in this paper. A modified Lyapunov–Krasovskii functional is constructed to study this class of systems. The proposed stability criterion is discrete-, distributed- and neutral-delay-dependent. In addition, by this method one can study the case when the coefficient matrix of the neutral delay term is time-varying uncertain. The reduced conservatism is illustrated in a numerical example.

A New Perspective in the Stability Assessment of Neutral Systems with Multiple and Cross-Talking Delays

The stability of neutral systems with two cross-talking delays is investigated using the method of cluster treatment of characteristic roots (CTCR). There are two main outcomes of this study: (a) we create the “strong stabilizability” (also called the “delay stabilizability”) of the system directly from the CTCR procedure. This is achieved by a small-delay stability treatment while performing the steps of the CTCR. For the “delay-stabilizable systems,” we also arrive at the exact bounds of the stability regions in the domain of the delays. (b) We deploy a point-wise algorithm which computes the rightmost roots of the characteristic quasi polynomial for cross-verification of these stability regions. Several examples are presented. The correspondence between the two methods for all of them is shown to be very strong.

On delay-dependent robust stability of neutral systems

The delay-dependent robust stability of uncertain linear neutral systems with delays is investigated. Both discrete-delay-dependent/neutral-delay-independent and neutral-/discrete-delay-dependent stability criteria will be developed. The proposed stability criteria are formulated in the form of linear matrix inequalities and it is easy to check the robust stability of the considered systems. By introducing certain Lyapunov-Krasovskii functional the mathematical development of our result avoids model transformation and bounding for cross terms, which lead to conservatism. Finally, numerical example is given to indicate the improvement over some existing results.

EXACT STABILITY ANALYSIS OF NEUTRAL SYSTEMS WITH CROSS-TALKING DELAYS

The stability of neutral systems with two cross-talking delays is investigated using the method of cluster treatment of characteristic roots (CTCR). There are two main outcomes of this study: (a) Generation of the well-known delay stabilizability condition as a by-product of the CTCR procedure. This is achieved by a small delay stability treatment over the system. We also demonstrate for the delay-stabilizable systems the exact bounds of the stability regions in the domain of the delays. (b) Validation of these stability regions using an alternative point-wise algorithm, which computes the right-most roots of the characteristic quasi-polynomial.

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.

Delay-dependent robust stability for neutral systems with mixed discrete-and-neutrai delays

This paper focuses on the problem of delay-dependent robust stability of neutral systems with different discrete-and-neutral delays and time-varying structured uncertainties. Some new criteria are presented, in which some free weighting matrices are used to express the relationships between the terms in the Leibniz-Newton formula. The criteria include the information on the size of both neutral-and-discrete delays. It is shown that the present results also include the results for identical discrete-and-neutral delays as special cases. A numerical example illustrates the improvement of the proposed methods over the previous methods and the influences between the discrete and neutral delays.