Systems Of Neutral Type Research Articles

Solvability and Optimal Control of Nonautonomous Fractional Dynamical Systems of Neutral-Type with Nonlocal Conditions

Solvability and Optimal Control of Nonautonomous Fractional Dynamical Systems of Neutral-Type with Nonlocal Conditions

Delay-dependent robust stability analysis of uncertain fractional-order neutral systems with distributed delays and nonlinear perturbations subject to input saturation

Abstract In this article, we address the delay-dependent robust stability of uncertain fractional order neutral-type (FONT) systems with distributed delays, nonlinear perturbations, and input saturation. With the aid of the Lyapunov–Krasovskii functional, criteria on asymptotic robust stability of FONT, expressed in terms of linear matrix inequalities, are constructed to compute the state-feedback controller gains. The controller gains are determined subject to maximizing the domain of attraction via the cone complementarity linearization algorithm. The theoretical results are validated using numerical simulations.

Lyapunov–Krasovskii functionals for homogeneous time delay systems of neutral type

AbstractIn this article, we present a general construction of Lyapunov–Krasovskii functionals for a class of neutral‐type time delay systems with a linear difference part and homogeneous right‐hand sides of degree strictly greater than one. Under an assumption that the corresponding difference matrix equation as well as a system with zero delays are asymptotically stable, the functionals allow proving delay‐independent asymptotic stability. They are based on the Lyapunov functions of the corresponding delay free systems and constitute a generalization of constructions presented recently for homogeneous systems of retarded type. The functionals are applied to the robustness analysis with respect to uncertainties at the right‐hand sides and at the difference term as well.

LMI-based stability analysis of fractional order systems of neutral type with time varying delays under actuator saturation

LMI-based stability analysis of fractional order systems of neutral type with time varying delays under actuator saturation

Estimates for Solutions to a Class of Nonautonomous Systems of Neutral Type with Unbounded Delay

Estimates for Solutions to a Class of Nonautonomous Systems of Neutral Type with Unbounded Delay

Further Robust Stability Analysis For Time-delayed Neutral-type Systems by a Modified Lyapunov-Krasovskii Functional

This paper further studies the stability of the uncertain delayed neutral-type system by constructing a novel Lyapunov-Krasovskii functional (LKF) with some delay-dependent and N-dependent items. Some new delay-dependent robust stability criteria are proposed based on linear matrix inequality (LMI). The criteria proposed in this paper are less conservative than some recent previous ones. Some numerical examples, including a linear neutral-type system, the partial element equivalent circuit and a general linear system, are presented to show the effectiveness of the proposed approach.

Relaxation of the attainability problem for a linear control system of neutral type

The problem of control of a linear system of neutral type with impulse constraints is developed. In addition, a given system of intermediate conditions is assumed. A setting is investigated in which a vanishingly small relaxation of the mentioned restrictions is allowed. In this regard, the attainability domain (AD) at a fixed time of the end of the process is replaced by a natural asymptotic analog, the attraction set (AS). To construct the latter, we use the construction of an extension in the class of finitely additive (f.-a.) measures used as generalized controls. It is shown that the AS coincides with the AD of the system in the class of generalized controls – f.-a. measures. The structure of the mentioned AS is investigated.

Stabilization of Delayed Fuzzy Neutral-type Systems Under Intermittent Control

This study is concerned about the stabilization for delayed fuzzy neutral-type system (DFNTS) with uncertain parameters under intermittent control. Firstly, by constructing the augmented Lyapunov-Krasovskii functional (LKF) about different time delays along with single and double auxillary function-based integral inequalities (SAFBII, and DAFBII, respectively), a new class of delay-dependent adequate conditions are proposed, so that the robust fuzzy neutral-type system under consideration is guaranteed to be globally asymptotically stable (GAS). Secondly, the intermittent control (IC) is introduced to stabilize the system with mixed time-varying delays. In the view of inferred adequate conditions, the IC parameters are determined as for the arrangement of linear matrix inequalities (LMIs). It is noted that the strategies exploited in this work are apart from the other methods engaged in the literature, and the proposed conditions are less conservative. Finally, numerical examples are given to demonstrate the effectiveness of the developed techniques in this work. One of the practical applications is single-link robot arm (SLRA) model to show the viability and benefits of the structured intermittent control.

Observer‐based control approach for fractional‐order delay systems of neutral type with saturating actuator

In practice the states of a system are not directly available that are difficult to measure by sensors. This article proposes an observer‐based controller for fractional‐order neutral‐type delay systems with actuator saturation. A feedback algorithm is constructed by applying the Lyapunov direct method. Moreover, based on the observer, the gains of controller and observer are determined by solving a set of nonlinear matrix inequalities. Therefore, an iterative algorithm including the convex optimization is also proposed to solve the inequalities. An example is given to illustrate the theoretical results.

Exact Reconstruction of the Solution for Linear Neutral Type Systems

Exact Reconstruction of the Solution for Linear Neutral Type Systems

A Guaranteed Cost Approach to Dynamic Output Feedback Control for Neutral-Type Markovian Jumping Stochastic Systems

This paper is devoted to investigating the dynamic output feedback (DOF) control problem of Markovian jump neutral-type stochastic systems with a guaranteed cost function. Both of the state and measurement equations contain time delays. Mode-dependent DOF controllers are first designed such that the closed-loop system is asymptotically stable in mean-square and an adequate performance level of this system is guaranteed. Then, sufficient conditions for the solvability of this problem are derived in the form of linear matrix inequalities (LMIs). A numerical example is presented to reveal the effectiveness of our findings.

Event-Triggered L 2–L ∞ Filtering for Network-Based Neutral Systems With Time-Varying Delays via T-S Fuzzy Approach

This article examines the issue of event-triggered $L_{2}-L_\infty $ filtering for network-based neutral systems via Takagi-Sugeno (T-S) fuzzy approach. A dynamic discrete event-triggered scheme (ETS) is introduced to save the limited communication resource. Based on the T-S fuzzy model, the consider neutral type system with networked induced delays are represented as a class of T-S fuzzy system. In addition, by considering a suitable Lyapunov-Krasovskii functional (LKF) and by using the Wirtinger inequality technique, the stability conditions with respect to linear matrix inequalities (LMIs) are presented to guarantee the considered filtering systems are asymptotically stable with $L_{2}-L_{\infty }$ performance index $\gamma $ . To the end, numerical examples are given to illustrate the effectiveness of the proposed result.

Exponential stability of Hopfield neural networks of neutral type with multiple time-varying delays

<abstract> This paper investigates the problem for exponential stability of Hopfield neural networks of neutral type with multiple time-varying delays. Different from the existing results, the states of the neurons involve multiple time-varying delays and time derivative of states of neurons also include multiple time-varying delays. The exponential stability of such neutral-type system has not been received enough attention since it is not easy to construct a suitable Lyapunov-Krasovskii functional to analyze the exponential stability of this type of neural system. Novel sufficient conditions of the exponential stability are established by using Lyapunov method and inequality techniques. Compared with some references, the mathematical expression of the neutral-type system is more general and the established algebraic conditions are less conservative. Three examples are given to demonstrate the effectiveness of the theoretical results and compare the established stability conditions to the previous results. </abstract>

Well-posedness and approximate controllability of neutral network systems

&lt;p style='text-indent:20px;'&gt;In this paper, we study the concept of approximate controllability of retarded network systems of neutral type. On one hand, we reformulate such systems as free-delay boundary control systems on product spaces. On the other hand, we use the rich theory of infinite-dimensional linear systems to derive necessary and sufficient conditions for the approximate controllability. Moreover, we propose a rank condition for which we can easily verify the conditions of controllability. Our approach is mainly based on the feedback theory of regular linear systems in the Salamon-Weiss sense.&lt;/p&gt;

Asymptotic properties and stabilization of a neutral type system with constant delay

The problem of obtaining sufficient conditions for the asymptotic stability for a certain class of linear systems of a neutral type with constant delay is analyzed in the article. Some coefficients of these systems in the right side have an exponential factor. As a consequence, the study of the stability of such systems with the help of the Lyapunov—Krasovskii functionals is not possible; methods of receiving asymptotic appreciations lead to extremely rough results. By applying the apparatus of difference systems and the properties of simpler systems, which the author examined previous, sufficient conditions for the exponential stability of such systems are obtained. As an example, a second-order system is considered. The graphs of the solutions of the corresponding system, both without neutral members and with the original system where the right-hand side contains neutral terms, are provided. On the basis of theory difference systems, the author proposes an algorithm of stabilization for some systems of a similar type.

On the Strong $\mathcal {H}_2$ Norm of Differential Algebraic Systems With Multiple Delays: Finiteness Criteria, Regularization, and Computation

The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_2$</tex-math></inline-formula> norm of an exponentially stable system described by delay differential algebraic equations (DDAEs) might be infinite due to the existence of hidden feedthrough terms and, as shown in this article, it might become infinite as a result of infinitesimal changes to the delay parameters. We introduce the notion of strong <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_2$</tex-math></inline-formula> norm of semi-explicit DDAEs, a robustified measure that considers delay perturbations, and we analyze its properties. We derive necessary and sufficient finiteness criteria for the strong <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_2$</tex-math></inline-formula> norm in terms of a finite number of equalities involving multidimensional powers of a finite set of matrices. As the main contribution, we present a strengthened, sufficient, condition for finiteness of the strong <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_2$</tex-math></inline-formula> norm, along with an algorithm for checking it, which has significantly better scalability properties in terms of both the system dimension and the number of delays. We show that the satisfaction of the novel condition is equivalent to the existence of a simultaneous block triangularization of the matrices of the delay difference equation associated with the DDAE. The latter is instrumental to a novel regularization procedure that allows us to transform the DDAE to a neutral-type system with the same transfer matrix, without any need for differentiation of inputs or outputs. This transformation enables computing of the strong <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_2$</tex-math></inline-formula> norm using Lyapunov matrices. Finally, we show by a counterexample that the strengthened condition is, in general, not necessary, inducing open problems, but we also list several classes of DDAEs for which it is necessary and sufficient.

On oscillatory second order nonlinear impulsive systems of neutral type

In this work, the necessary and sufficient conditions for oscillation of a class of second order neutral impulsive systems are established and our impulse satisfies a discrete neutral nonlinear equation of similar type. Further, one illustrative example showing applicability of the new result is included.

Robust stability of uncertain fractional order systems of neutral type with distributed delays and control input saturation

Time delay occurs naturally due to the limited bandwidth of any real-world system. However, this problem can deteriorate the system performance and can even result in system instability. Input saturation is also an essential issue due to the energy constraint in real actuators that makes the control design procedure more difficult. This article concerns with the stability of uncertain fractional order (FO) delay systems of neutral type including structured uncertainties, distributed delays and actuator saturation. A Lyapunov–Krasovskii functional allows the formulation of the conditions to insure the asymptotic robust stability of such systems via the linear matrix inequalities (LMI) and to compute the gain of a state feedback controller. In addition, by using the cone complementarity linearization method, we obtain the controller gains that extend the domain of attraction. Several simulations validate the theoretical analysis.

Exponential Stability Using Sliding Mode Control for Stochastic Neutral-Type Systems

This study deals with the exponential stability of stochastic neutral-type systems (SNTSs) with Markovian switching and Levy noises. A new integral sliding mode surface for SNTSs is constructed to design a sliding mode controller. Furthermore, a new Lyapunov function is assigned to obtain the exponential stability criterion of SNTSs. On this basis, a new sliding mode control law is proposed to ensure the accessibility of SNTSs. In addition, the parameters of the sliding mode controller for SNTSs are obtained. Finally, an example to illustrate the theoretical results has been presented.

Necessary and Sufficient Stability Condition by Finite Number of Mathematical Operations for Time-delay Systems of Neutral Type

We present a new necessary and sufficient condition of exponential stability of neutral-type linear time invariant (LTI) systems with one delay. The new stability criterion is given in terms of a block matrix, which exclusively depends on the delay Lyapunov matrix and is of finite dimension.