Systems Of Neutral Type Research Articles

Estimates of Solutions for a Class of Nonautonomous Systems of Neutral Type with Concentrated and Distributed Delays

Estimates of Solutions for a Class of Nonautonomous Systems of Neutral Type with Concentrated and Distributed Delays

On the issue of control of neutral-type systems by hybrid controllers with state feedback

For linear autonomous systems of neutral type, an approach to control design problems in the form of feedback based on a new class of hybrid controllers is proposed. The structure of hybrid regulators necessarily includes a differential equation, so the closed system becomes differential-algebraic. A distinctive feature of hybrid controllers is the existence of elementary transformation of equations of a closed-loop system, which make it possible to obtain an independent subsystem of neutral type. In this case, the specified subsystem of neutral type uniquely determines the behavior of the solution $x(t)$ of the original open-loop system (possibly as a vector component of the solution vector of the closed-loop system). The main advantages of using hybrid controllers include the possibility of their application to systems that do not satisfy the “traditional” controllability properties. The properties of hybrid controllers have been studied. The author gives an example of using these controllers to solve a new problem of controlling the coefficients of a characteristic quasi-polynomial in the case where the approaches known in the literature are not applicable. The possibility of using hybrid controllers to solve the $0$-controllability problem using the finite control method is demonstrated.

Stability analysis of a class of variable fractional-order uncertain neutral-type systems with time-varying delay

Variable fractional-order (VFO) differential equations are a beneficial tool for describing the nonlinear behavior of complex dynamical phenomena. In comparison with the constant FO derivatives, it describes the memory properties of such systems that can vary in the time domain and spatial location. This article investigates the stability and stabilization of VFO neutral systems in the presence of time-varying structured uncertainties and time-varying delay. FO Lyapunov theorem is adopted to achieve order-dependent and delay-dependent criteria for both nominal and uncertain VFO neutral delay systems. The obtained conditions are given in respect of linear matrix inequality by designing a delayed state feedback controller. Simulations verify the main results.

Stability analysis of fractional reaction-diffusion memristor-based neural networks with neutral delays via Lyapunov functions

In the realm of stability analysis for fractional neutral neural networks, it is not uncommon to encounter erroneous Lyapunov functions. To investigate the stability of fractional memristor-based neural networks with neutral delays and reaction–diffusion (FNRDMNNs), this study presents a novel modified Lyapunov–Krasovskii functions. By invoking Green’s theorem and employing inequality techniques, we derive two nonconservative criteria and a corollary through the design of two enhanced pinning controllers, ensuring the stability of FNRDMNNs. Furthermore, the contributions of this paper not only serve as refinements to existing findings but also hold broader applicability for advancing the theoretical analysis of fractional neutral-type systems. To corroborate the obtained results, we perform a series of simulations.

Viscosity Solutions of Hamilton–Jacobi Equations for Neutral-Type Systems

Viscosity Solutions of Hamilton–Jacobi Equations for Neutral-Type Systems

Disturbance observer-based delayed robust feedback control design for a class of uncertain variable fractional-order systems: Order-dependent and delay-dependent stability

This work addresses the stabilization of variable fractional-order (VFO) neutral-type systems with structure perturbations and unknown disturbance signals using the feedback control approach. The goal is to design disturbance-observer-based delayed state- and output-feedback controllers to achieve robust stability of such VFO systems. The proposed controller consists of two parts, namely a primary controller based on the linear feedback technique, and an auxiliary controller based on the disturbance observer. A disturbance observer is developed to estimate the disturbance signal, which is generated by an exogenous system. Based on matrix inequalities, order-dependent and delay-dependent conditions are formulated via FO Lyapunov theory that guarantee the robust stability of the closed-loop system. Simulations verify the main results.

A Time-Delay Approach to Extremum Seeking with Large Measurement Delays*

In this paper, we present a time-delay approach to gradient-based extremum seeking (ES) with known large distinct measurement delays, for N-dimensional (ND) static quadratic maps. We assume that the Hessian has a nominal known part and norm-bounded uncertainty, the extremum point belongs to a known ball, and the extremum value to a known interval. By using the orthogonal transformation, we first transform the original static quadratic map into a new one with the Hessian containing a nominal diagonal part. By applying a time-delay approach to the resulting ES system, we arrive at the neutral type system with a nominal linear time-delay system. We further present this system as a retarded one and employ variation of constants formula for practical stability analysis. To obtain tight bounds we exploit positivity of the fundamental matrix that corresponds to the nominal system with delays. Explicit conditions in terms of simple scalar inequalities depending on tuning parameters and delay bounds are established to guarantee the practical stability of the ES control systems. An example from the literature illustrates the efficiency of the new approach.

Some estimates on the exponential stability of solutions of nonlinear neutral type systems with periodic coefficients

Some estimates on the exponential stability of solutions of nonlinear neutral type systems with periodic coefficients

A Time-delay Approach for Extremum Seeking of Nonlinear Static Maps:

This paper develops a constructive time-delay approach to averaging for gradient-based extremum seeking (ES) control of nonlinear static maps of non-quadratic form. Under the assumption that some prior knowledge of the nonlinear map with its derivatives is available, for the first time, we derive a quantitative analysis for ES close-loop systems with upper bounds on the tuning parameter that preserves the exponential stability and on the convergence error of extremum seeking. By transforming the ES system into a time-delay neutral type system with distributed delays, the developed method gives an accurate perturbed system of ES without employing any approximate calculation, and suggests a direct Lyapunov-Krasovskii approach in the form of linear matrix inequalities (LMIs), for the transformed time-delay plant to derive efficient stability conditions.

Asymptotic Properties of Some Neutral Type Systems with Linear Delay

Asymptotic Properties of Some Neutral Type Systems with Linear Delay

New Delay-Partitioning LK-Functional for Stability Analysis with Neutral Type Systems

This paper investigates the stability issues associated with neutral-type delay systems. Firstly, the delay-partitioning method is employed to construct a brand-new LK-functional candidate. The discrete delay and a neutral delay are divided into several piecewise points through a relaxable sequence of constant numbers, are increasing at a steady rate and are not larger than 1. Secondly, to fully use the interconnection information among the delayed state vectors, a new LK-functional is constructed. Thirdly, the recently published single/multiple integral inequalities are employed to bound the derivative of the newly developed LK function. Finally, a novel stability criterion for neutral systems is developed based on the above treatment. Furthermore, a new corollary is also proposed for the condition of τ=h. The benefits and productivities of our method are demonstrated by numerical examples.

Multiplicity–Induced–Dominancy property for second–order neutral differential equations with application in oscillation damping

This paper addresses the exponential stability of linear time-delay systems of neutral type. In general, it is quite a challenge to establish conditions on the parameters of the system in order to guarantee such a stability. Recent works emphasized the link between maximal multiplicity and dominant roots. Indeed, conditions for a given multiple root to be necessarily dominant are investigated, this property is known as Multiplicity-Induced-Dominancy (MID). The aim of this paper is to explore the effect of multiple roots with admissible multiplicities exhibiting, under appropriate conditions, the validity of the MID property for second-order neutral time-delay differential equations with a single delay. The ensuing control methodology is summarized in a five-steps algorithm that can be exploited in the design of higher-order systems. The main ingredient of the proposed method is the dominancy proof for multiple spectral values based on frequency bounds established via integral equations. As an illustration, the stabilization of the classical oscillator benefits from the obtained results.

An improved finiteness test and a systematic procedure to compute the strong [formula omitted] norm of differential algebraic systems with multiple delays

We study the strong ℋ2 norm of systems modeled by semi-explicit Delay Differential Algebraic Equations (DDAEs). We recall that the finiteness of the strong ℋ2 norm is linked to an algebraic decision problem that can be solved by checking a finite numbers of equalities. We first improve the verification of the finiteness condition. In particular, the complexity of our new condition removes a dependency on the number of delays. We also show that, without imposing further conditions on the system, the number of checks cannot be further reduced. The methodology relies on interpreting the verification of the finiteness conditions in terms of a Polynomial Identity Testing problem. Second we show, in a constructive way, that if the strong ℋ2 norm is finite, the system can always be transformed into a regular neutral-type system with the same ℋ2 norm, without derivatives in the input or in the output equations. This result closes a gap in the literature as such a transformation was known to exist only under additional assumptions on the system. The transformation enables the computation of the strong ℋ2 norm using delay Lyapunov matrices. Illustrative examples are provided throughout the paper.

Finite Time Stability of Fractional Order Systems of Neutral Type

This work deals with a new finite time stability (FTS) of neutral fractional order systems with time delay (NFOTSs). In light of this, FTSs of NFOTSs are demonstrated in the literature using the Gronwall inequality. The innovative aspect of our proposed study is the application of fixed point theory to show the FTS of NFOTSs. Finally, using two examples, the theoretical contributions are confirmed and substantiated.

Synchronization of Multi-Agent Systems under Time-Varying Network via Time-Delay Approach to Averaging

This paper studies the leader-tracking problem of Multi-Agents Systems under a periodic time-varying communication topology, without requiring the connectivity of the network for all t ≥ 0. The case of both state and communication delays is considered. A fully distributed control protocol, along with the constructive time-delay approach to periodic averaging, are combined in order to solve the problem, thus ensuring that a time-dependent switching control rule preserves the input-to-state stability (ISS) of the entire network, despite the presence of disconnected topologies, state and communication delays. The original closed-loop error systems is transformed into a neutral-type system with discrete and distributed delays. ISS analysis of the neutral system employs appropriate Lyapunov-Krasovskii functionals leading to simple ISS conditions in terms of Linear Matrix Inequalities (LMIs), whose solution allows finding upper bounds on small parameter, state and communication delays that preserve ISS. Numerical simulations illustrate the effectiveness of the theoretical results.

Simultaneous actuator and sensor fault estimation for neutral-type systems via intermediate observer

This study addresses the fault estimation (FE) issue for neutral-type systems with sensor faults and actuator faults through the intermediate observer. First, it is well-known that the observer matching condition (OMC) ought to be met for most traditional FE methods, which is actually difficult to satisfy for many systems. In order to overcome this limitation, a suitable variable is designed and the intermediate observer is proposed to estimate the actuator and sensor faults for neutral-type systems simultaneously. Second, based on linear matrix inequalities, sufficient conditions are derived, which guarantee the existence of the intermediate observer. An augmented descriptor system is constructed for the neutral-type systems. By the Lyapunov stability theory, states of error systems are ultimately bounded. Finally, two examples demonstrate the effectiveness and practicability of the designed strategy.

Stability Analysis of Coupled Differential-Difference Systems With Multiple Time-Varying Delays:A Positivity-Based Approach

This article introduces novel results on linear coupled differential-difference systems with multiple time-varying delays. First, necessary and sufficient conditions for the positivity and delay-independent asymptotic stability of such systems are introduced. Then, exploiting the internally positive representation technique, we show how such stability results can be systematically exported to non-positive systems of the same class, yielding novel explicit sufficient conditions for their delay-independent stability. As a consequence, novel stability results on neutral-type systems, differential systems, and continuous-time difference systems with multiple delays are also obtained.

Stability of Solutions to One Class of Neutral Type Systems of Linear Autonomous Equations with Distributed Delay

Stability of Solutions to One Class of Neutral Type Systems of Linear Autonomous Equations with Distributed Delay

Asymptotic Analysis of Spectrum and Stability for One Class of Singularly Perturbed Neutral-Type Time-Delay Systems

In this study, a singularly perturbed linear time-delay system of neutral type is considered. It is assumed that the delay is small of order of a small positive parameter multiplying a part of the derivatives in the system. This system is decomposed asymptotically into two much simpler parameter-free subsystems, the slow and fast ones. Using this decomposition, an asymptotic analysis of the spectrum of the considered system is carried out. Based on this spectrum analysis, parameter-free conditions guaranteeing the exponential stability of the original system for all sufficiently small values of the parameter are derived. Illustrative examples are presented.

On exact controllability and complete stabilizability for linear systems

In this paper we consider linear systems with control described by the equation $\dot x = \mathcal A x +\mathcal B u$ where functions u and x take values in U and X respectively. For such object, a short review of results concerning relations between exact controllability and complete stabilizability (stabilizability with arbitrary decay rate) is given. The analysis is done in various situations: bounded or unbounded state and control operators $\mathcal A$ and $\mathcal B$, Banach or Hilbert spaces U and X. The well known equivalence between complete controllability and pole assignment in the situation of finite dimensional spaces is no longer true in general in infinite dimensional spaces. Exact controllability is not sufficient for complete stabilizability if U and X are Banach spaces. In Hilbert space setting this implication holds true. The converse also is not so simple: in some situations, complete stabilizability implies exact controllability (Banach space setting with bounded operators), in other situation, it is not true. The corresponding results are given with some ideas for the proofs. Complete technical development are indicated in the cited literature. Several examples are given. Special attention is paid to the case of infinite dimensional systems generated by delay systems of neutral type in some general form (distributed delays). The question of the relation between exact null controllability and complete stabilizability is more precisely investigated. In general there is no equivalence between the two notions. However for some classes of neutral type equations there is an equivalence. The question how the equivalence occurs for more general systems is still open. This is a short and non exhaustive review of some research on control theory for infinite dimensional spaces. Our works in this area were initiated by V. I. Korobov during the 70th of the past century in Kharkov State University.