A delay-dependent stability criterion for linear neutral delay systems

A new stability criterion for linear neutral delay systems is developed in this note. Based on Park's inequality, a new delay-dependent stability criterion is derived. A numerical example is proposed to illustrate the less conservatism of the obtained results.     

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.     

Further results on asymptotic stability of linear neutral systems with multiple delays

The problem of asymptotic stability of linear neutral systems with multiple delays is addressed in this article. Using the characteristic equation approach, new delay-independent stability criteria are derived in terms of the spectral radius of modulus matrices. The structure information of the system matrices are taken into consideration in the proposed stability criteria, thus the conservatism found in the literature can be significantly reduced. Simple examples are given to demonstrate the validity of the criteria proposed and to compare them with the existing ones.     

On linear generalized neutral differential delay systems

In this paper, the class of linear generalized neutral differential delay systems with time-invariant coefficients is studied. These kinds of systems are inherent in many physical and engineering phenomena. Using the matrix pencil theory, we decompose it into five subsystems, whose solutions are obtained. Moreover, the form of the initial function is given, so the corresponding initial value problem is uniquely solvable.     

A necessary and sufficient condition for delay-independent stability of linear time-varying neutral delay systems

In this paper, stability analysis of linear time-varying neutral delay systems is considered. A necessary and sufficient condition for delay-independent global asymptotic stability of such systems is derived. Eventually, two examples are given in order to show the results established.     

New criterion for finite-time stability of linear discrete-time systems with time-varying delay

This paper is concerned with the problem of finite-time stability analysis of linear discrete-time systems with time-varying delay. The time-varying delay has lower and upper bounds. By choosing a novel Lyapunov–Krasovskii-like functional, a new sufficient condition is derived to guarantee that the state of the system with time-varying delay does not exceed a given threshold during a fixed time interval. Then, the corresponding corollary is developed for the case of constant time delay. Numerical examples are provided to demonstrate the effectiveness and merits of the proposed method.     

Another sufficient condition for the stability of grey discrete-time systems

In this paper, the stability of grey discrete-time systems is discussed whose state matrices are interval matrices. A new approach is obtained which guarantee the stability of grey discrete-time systems. The sufficient condition for robust stability of grey time delay systems subjected to interval systems is also derived. By mathematical analysis, the stability criterion is less conservative than those in previous results. Examples are given to compare the proposed method with reported recently.     

Necessary conditions for exponential stability of linear neutral type systems with multiple time delays

In this paper, we will give necessary conditions for the exponential stability of linear neutral type systems with multiple time delays by employing the Lyapunov–Krasovskii functional approach. These conditions not only extend the existing results of the neutral-delay-free systems, but also provide a new tool for stability analysis of linear neutral type systems with multiple time delays by characterizing instability domains. As a medium step, we will investigate several crucial properties which are involved with both the fundamental matrix and Lyapunov matrix. Numerical examples illustrate the validity of the theoretical results.     

A neutral system approach to stability of singular time-delay systems

This paper is concerned with the problem of delay-dependent stability for a class of singular time-delay systems. By representing the singular system as a neutral form, using an augmented Lyapunov–Krasovskii functional and the Wirtinger-based integral inequality method, we obtain a new stability criterion in terms of a linear matrix inequality (LMI). The criterion is applicable for the stability test of both singular time-delay systems and neutral systems with constant time delays. Illustrative examples show the effectiveness and merits of the method.     

An improved delay-dependent stability criterion of networked control systems

This paper presents a new stability analysis of networked control systems (NCSs) with network-induced delay and packet dropout. A novel augmented Lyapunov–Krasovskii functional (LKF) is constructed, which takes into account the feature of the sawtooth delay induced by sample-and-hold. Based on an improved version of Wirtinger's inequality and the convex combination method, a delay-dependent stability criterion is derived in terms of linear matrix inequalities (LMIs). The advantage of the proposed criterion lies in its simplicity and less conservativeness than some of the existing results. The new criterion is applied to the network-based state feedback control problems. Numerical examples are given to verify the effectiveness of the proposed criterion.     

Strong delay-independent stability of linear delay systems

This paper presents a new necessary and sufficient condition for testing the strong delay-independent stability of linear systems subject to a single delay. The proposed method follows from the use of matrix polynomials constraints and the Kalman–Yakubovich–Popov lemma. The resulting condition can be checked exactly by solving a feasibility problem in terms of a linear matrix inequality (LMI). Simple numerical examples are given to show the effectiveness of the proposed method.     

Chaotification of a class of linear switching systems based on a Shilnikov criterion

This paper proposes an approach for constructing and generating chaos from a class of three-dimensional linear switching systems via a heteroclinic loop based on the Shilnikov criterion. First, the existence of a switching rule for the system is derived by utilizing the Shilnikov heteroclinic criterion. Then a general design philosophy and its procedure of switching rule are provided to ensure that the proposed approach is applicable to engineering. Two numerical examples are presented to validate the main principle and the implementability of the scheme. Theoretical analysis and numerical simulation are used to demonstrate the feasibility and effectiveness of developed techniques.     

Modification of Mikhailov stability criterion for fractional commensurate order systems

In this paper we present the modification of the Mikhailov stability criterion for linear fractional commensurate order systems. The modification consists in determining the appropriate measure for the total argument change depending on the highest fractional order ${\alpha }_n=n\alpha$ of the system and not only on the integer n as stated in the literature. The validity of the result is illustrated by means of several examples.     

A novel approach to stability analysis for switched positive linear systems

This paper is concerned with exploring less conservative stability conditions for a class of switched positive linear systems. A switched matrix-parameterized copositive Lyapunov function (SMPCLF) is first introduced, where “matrix-parameterized” implies that the parameters of the constructed Lyapunov function are distributed in a matrix, which is different from the traditional vector-parameterized copositive Lyapunov function. Based on the proposed SMPCLF, a new stability criterion is derived for the underlying systems under arbitrary switching. Furthermore, by performing higher order relaxations in the SMPCLF and its time difference by positive states, the conservativeness can be further reduced. A numerical example is given to demonstrate the effectiveness and advantages of the obtained theoretical results.     

Robust stability of uncertain second-order linear time-varying systems

This paper is concerned with robust stability analysis of second-order linear time-varying (SLTV) systems with time-varying uncertainties (perturbations). With the specific Lyapunov functions, a simple and neat algebraic criterion for testing uniformly asymptotic stability of SLTV systems are derived. Without transformation to a system of first-order equations, the new conditions are imposed directly on the time-varying coefficient matrices of the system. The main feature of the proposed algebraic criterion is that the uncertain coefficient matrices are time-varying and not necessarily symmetric. Finally, the proposed stability conditions are used to design the extending space structures system of the spacecraft. Simulation results are provided to illustrate the convenience and effectiveness of the proposed method.     

A delay-variation-dependent stability criterion for discrete-time systems via a bivariate quadratic function negative-determination lemma

This article concerns with stability analysis of discrete linear systems with time-varying delays. Firstly, we extend a quadratic function negative-determination lemma for a single variable to the bivariate case. Secondly, we construct a novel Lyapunov-Krasovskii functional (LKF) with a quadratically delay-dependent matrix to investigate the stability of discrete-time systems with time-varying delays. Based on the proposed lemma, a new delay-variation-dependent stability criterion is derived. Finally, numerical examples are given to illustrate the theoretical result and the proposed criterion is shown to be less conservative than some previous ones.     

New results on BIBO stability analysis for a class of neutral delay systems

This paper studies bounded input bounded output (BIBO) stability for a class of neutral systems with time-varying delays. Based on Lyapunov method and linear matrix inequalities, some new BIBO stability criteria are established. The numerical simulation is made to demonstrate the effectiveness of the theoretical results obtained in this paper.     

Uniform asymptotic stability of linear time-varying singularly perturbed systems

An upper bound for the singular perturbation parameter is found for the uniform asymptotic stability of singularly perturbed linear time-varying systems.     

A note on existence of a unique periodic solution of non-autonomous second-order Hamiltonian systems

In this study, we shall be concerned with a non-autonomous second-order Hamiltonian system. Some criteria for guaranteeing the existence and uniqueness of T-periodic classical solution of this system are presented by employing the least action principle, the Saddle Point Theorem and some analysis techniques.