Neutral Singular Systems Research Articles

New results on the stability and stabilization for singular neutral systems with time delay

The stability issue and stabilization issue for a class of singular neutral systems are studied in this paper. Firstly, we give some sufficient conditions such that the considered open-looped systems are admissible. Secondly, we give some results which design the feedback controllers and ensure that the resulting close-looped systems are admissible. Finally, the superiority and effectiveness of the obtained methods are illustrated by two numerical examples. The results obtained in this paper can be employed to analyze the singular neutral systems which do not satisfy the restrictive conditions presented in some published papers.

Finite-time stability analysis of singular neutral systems with time delay

<p>This paper studies the finite-time stability problem for a class of singular neutral systems by using the Lyapunov-Krasovskii function approach and regular neutral system theory. The considered systems involve not only the delayed version of the state, but also the delayed version of the derivative of the state. Some sufficient conditions are presented to ensure that the considered systems are regular, impulse-free, and finite-time stable. Three numerical examples are given to illustrate the effectiveness of the proposed methods.</p>

A study on the admissibility of fractional singular systems with variable and constant delays

This paper deals with fractional singular systems with mixed delays and several admissibility criteria are obtained by using Lyapunov-Krasovskii functionals, model transformation, useful lemmas, zero equations and other well-known inequalities. Finally, some numerical examples are given with graps to verify and justify the admissibility of practical systems by using our proposed methods.

Exponentially admissibility of neutral singular systems with mixed interval time-varying delays

The chief aim of this paper is to analyze the exponentially admissibility of neutral singular systems (NSSs) with mixed interval time-varying delays (TVDs). A new Lyapunov-Krasovskii functional (LKF) is presented based on state decomposition method. Via adopting linear matrix inequality (LMI) method and zero-value equation technology, a novel delay-dependent exponentially admissibility criterion is acquired. Furthermore, the exponentially admissibility analysis of the NSSs with equal mixed TVDs is discussed. Three numerical examples show that our method is effective and superior. In particular, the reasonable analysis and design for two practical application models (direct current (DC) motor model and oil catalytic cracking process (OCCP) model) illustrate that our research is very meaningful.

Further results on delay-dependent stability for neutral singular systems via state decomposition method

Abstract This paper studies the delay-dependent stability for neutral singular systems. In the light of state decomposition method, a novel augmented Lyapunov-Krasovskii functional including less decision variables is developed. Then by means of zero-value equations technology, some sufficient stability conditions in the form of linear matrix inequalities are acquired, which guarantees the non-impulsiveness, regularity and stability for the proposed neutral singular systems. The obtained stability criterion takes the sizes of both the discrete- and neutral- delays into account. They are less conservative than those presented by previous analytical approaches. Numerical examples are given to show the feasibility of our method and the interrelation between the discrete- and neutral- delays.

New results on stability analysis for a kind of neutral singular systems with mixed delays

In this paper, the problem of the stability analysis for neutral singular systems with mixed delays is revisited. By the Lyapunov–Krasovskill functional approach and the singular system methodology, novel stability criteria are acquired, which can be easily expressed by linear matrix inequalities. First of all, in terms of Leibniz–Newton formula, zero equation with free-weighting matrices is fully constructed, which plays a key role in the field of stability analysis and makes the stability criterion feasible. Secondly, the asymptotically stability for neutral singular systems is strictly shown, which is different from other existing results. Thirdly, the regularity, non-impulsiveness and stability can be guaranteed based on some sufficient conditions. Finally, three numerical examples and simulation studies are presented to demonstrate the validity and feasibility of our method.

Exponential stability analysis for a class of neutral singular Markovian jump systems with time-varying delays

This paper deals with the exponential stability problem for a class of neutral singular systems with Markovian jump parameters. The considered systems involve time-varying delays not only in their state but also in their derivatives of state. By using the Lyapunov–Krasovskii functional method, some sufficient conditions are derived, which ensure that the considered systems are regular, impulse-free and exponentially stable. Finally, some numerical examples are employed to demonstrate the effectiveness of the obtained approaches.

Delay-dependent robust absolute stability of uncertain Lurie singular systems with neutral type and time-varying delays

This paper is concerned with the robust absolute stability analysis for Lurie control of the neutral singular systems. By using Lyapunov–Krasovskii function method, delay dependent criteria for absolute stability of system are derived in terms of Linear Matrix Inequality. The difference between this paper and other existing results is that the lower bounds and upper bounds of discrete-delay are considered, which will obtain some less conservative stability analysis results. Finally, some numerical examples are presented to illustrate the effectiveness of the method.

H∞ Sampled-Data Control for Singular Neutral System

This study is concerned with the H∞ control problem for singular neutral system based on sampled-data. By input delay approach and a composite state-derivative control law, the singular system is turned into a singular neutral system with time-varying delay. Less conservative result is derived for the resultant system by incorporating the delay decomposition technique, Wirtinger-based integral inequality, and an augmented Lyapunov-Krasovskii functional. Sufficient conditions are derived to guarantee that the resulting system is regular, impulse-free, and asymptotically stable with prescribed H∞ performance. Then, the H∞ sampled-data controller is designed by means of linear matrix inequalities. Finally, two simulation results have shown that the proposed method is effective.

PD feedback H ∞ $H_{\infty}$ control for uncertain singular neutral systems

This paper focuses on the problem of proportional-plus-derivative (PD) feedback $H_{\infty}$ control for uncertain singular neutral systems. The parameter uncertainties are assumed to be time-varying norm-bounded and appearing not only in the state matrix but also in the derivative matrix. This paper introduces new effective criteria which make the systems stable and meet the $H_{\infty}$ performance by PD feedback controller. Different from most existing methods, this study attempts to introduce the information between derivative matrices. Based on such an idea, the PD feedback controller for singular neutral systems is first of all proposed which makes the derivative matrices (especially neutral matrix) meet the requirement which guarantees the existence of the solution for the system. So the criteria in this paper are less conservative to some extent. Finally, illustrate examples are given to demonstrate the effectiveness of the proposed approach.

Robust stability analysis and stabilisation of uncertain neutral singular systems

ABSTRACTThis paper studies the problem of robust stability and stabilisation of uncertain neutral singular systems and develops a new stability criterion of the differential operator, ℑ by the final value theorem for Laplace transform. By utilising Lyapunov functional and free-weight matrix method, we employ the linear matrix inequality technique and the stability condition to derive some new criteria which ensure the robustly asymptotical stability of the studied system. State feedback controllers with disturbance are designed to guarantee the robustly asymptotical stability of the uncertain system. Numerical examples are provided to validate the effectiveness of the obtained results.

Output Strictly Passive Control of Uncertain Singular Neutral Systems

This paper concerns the problem of output strictly passive control for uncertain singular neutral systems. It introduces a new effective criterion to study the passivity of singular neutral systems. Compared with the previous approach, this criterion has no equality constraints. And the state feedback controller is designed so that the uncertain singular neutral systems are output strictly passive. In terms of a linear matrix inequality (LMI) and Lyapunov function, the strictly passive criterion is formulated. And the desired passive controller is given. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed approach.

Asymptotic stability of nonlinear fractional neutral singular systems

In this paper, fractional calculus has been introduced into neutral singular systems. The (asymptotical) stability and (generalized) Mittag-Leffler stability of nonlinear fractional neutral singular systems with Caputo and Riemann-Liouville derivatives are studied, respectively. Several sufficient conditions guaranteeing stability of such systems are established by using the Lyapunov direct method.

Mittag–Leffler stability of nonlinear fractional neutral singular systems

This paper studies Mittag–Leffler stability of nonlinear fractional neutral singular systems under Caputor and Riemann–Liouville derivatives. Several sufficient conditions are derived by extending Lyapunov direct method to such systems. Our theoretical results can also be applied to general fractional retarded, neutral and singular systems.

A matrix method for determining the imaginary axis eigenvalues of a delay system

The author considers autonomous neutral or retarded matrix delay differential systems. The imaginary axis eigenvalues of such a system are shown to be contained in the set of generalized eigenvalues of an associated matrix pair. If the system is not a singular neutral system, one can replace generalized eigenvalues by the eigenvalues of a single matrix. We also show in both the neutral and retarded cases that system pure imaginary eigenvalues are limited to the values at which an associated second degree matrix polynomial becomes singular. Associated system eigenvectors are also eigenvectors of this matrix polynomial. Examples are given in which the matrix, the matrix pair, and the matrix polynomial are used for stability analysis.