2 edition of **Stability of finite and infinite dimensional nonlinear delay systems, indepenedent ogthe delay** found in the catalog.

Stability of finite and infinite dimensional nonlinear delay systems, indepenedent ogthe delay

Banks, Stephen P.

- 174 Want to read
- 14 Currently reading

Published
**1996** by University of Sheffield, Dept. of Automatic Control and Systems Engineering in Sheffield .

Written in English

**Edition Notes**

Statement | S.P.Banks, and D.McCaffrey. |

Series | Research report / University of Sheffield. Department of Automatic Control and Systems Engineering -- no.642, Research report (University of Sheffield. Department of Automatic Control and Systems Engineering) -- no.642. |

Contributions | McCaffrey, D. |

ID Numbers | |
---|---|

Open Library | OL16579330M |

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Nonlinear Delay SystemS, Independent of the Delay and rey University of Sheffield, Mappin Street, Sheffield 3JD Research Report No Abstract:The stability of nonlinear delay systems is considered.

General conditions on pseudo-linear finite- and infinite-dimensional delay systems are given for stability independent of. Read "Stability of finite-dimensional and infinite-dimensional nonlinear delay systems, independent of the delay, IMA Journal of Mathematical Control and Information" on DeepDyve, the largest online rental service for scholarly research with thousands of.

The aim of Stability of Finite and Infinite Dimensional Systems is to provide new tools for specialists in control system theory, stability theory of ordinary and partial differential equations, and differential-delay equations.

Stability of Finite and Infinite Dimensional Systems is the first book that gives a Stability of finite and infinite dimensional nonlinear delay systems exposition of the approach to stability analysis which is based on. () Finite-Time Stability and Stabilization of Nonlinear Singular Time-Delay Systems via Hamiltonian method.

Journal of the Franklin Institute. () Finite-time adaptive robust control of nonlinear time-delay uncertain systems with by: Request PDF | Finite‐time stability of switched nonlinear time‐delay systems | This article addresses the problem of finite‐time stability (FTS) and finite‐time contractive stability (FTCS.

where f denotes a nonlinear function. For example, in the Mackey–Glass equation, we have f(x, x τ) = βx τ /(1 + x n τ) − γx with the fixed parameters β, n and capture the effects of the time delay one needs a description which takes the history of the system into account, and thus requires a dynamical system with an infinite-dimensional phase space.

Although the last decade has witnessed significant advances in control theory for finite and infinite dimensional systems, Delay-independent stability of linear neutral systems: A riccati equation approach. Numerics of the stability exponent and eigenvalue abscissas of a matrix delay system.

Delay-independent stability of linear neutral systems: A riccati equation approach.- controllers for linear time-delay systems via infinite-dimensional Linear Matrix Inequality (LMI) approach. Stability of Finite Difference Methods In this lecture, we analyze the stability of ﬁnite differenc e discretizations.

First, we will discuss the Courant-Friedrichs-Levy (CFL) condition for stability of ﬁnite difference meth ods for hyperbolic equations. Then we will analyze stability more generally using a matrix approach.

51 Self-Assessment. We consider the question of when delay systems, which are intrinsically infinite dimensional, can be represented by finite dimensional systems. Specifically, we give conditions for when all the information about the solutions of the delay system can be obtained from the solutions of a finite system of ordinary differential equations.

For linear autonomous systems and linear systems. Finite Dimensional State Representation of Linear and Nonlinear Delay Systems: can be represented by finite dimensional systems. Specifically, we give conditions indepenedent ogthe delay book when all the information about the solutions of the delay system can be obtained from the solutions of a finite system of ordinary differential equations.

For linear autonomous. For more recent contributions on numerical methods for impulsive delay systems, oscillating system with pure delay, relative controllability of system with pure delay, asymptotic stability of nonlinear multi-delay differential equations, finite time stability of differential equations, one can refer to Khusainov & Shuklin (), Khusainov et al.

Spectral Analysis and Multigrid Methods for Finite Volume Approximations of Space-Fractional Diffusion Equations Effects of impulse delays on L-stability of a class of nonlinear time-delay systems. Journal of the Franklin InstituteStability of nonlinear infinite dimensional impulsive systems and their interconnections.

This paper investigates two different temporal finite element techniques, a multiple element (h-version) and single element (p-version) method, to analyze the stability of a system with a time-periodic coefficient and a time delay.

This paper is concerned with the problems of finite-time stability (FTS) and finite-time stabilisation for a class of nonlinear systems with time-varying delay, which can be represented by Takagi–Sugeno fuzzy system.

Some new delay-dependent FTS conditions are provided and applied to the design problem of finite-time fuzzy controllers. The existence of time-delay causes performance deterioration and even instability of practical control on this, many researches have been performed on the stability and stabilization for non-switched nonlinear time-delay systems on the basis of two methods: the Lyapunov–Krasovskii method and the Lyapunov–Razumikhin method in [5,23,37,45,46].Moreover, it is often impossible to.

This paper investigates the finite-time stability problem of a class of nonlinear fractional-order system with the discrete time delay. Employing the Laplace transform, the Mittag-Leffler function and the generalised Gronwall inequality, the new criterions are derived to guarantee the finite-time stability of the system with the fractional.

Analysing the corresponding delay differential equations is necessary to design control algorithms. 1 Time delay‐induced vibrations may occur in many applications, including traffic dynamics, 2 population dynamics, 3 gene regulatory networks, 4 and machine tool vibrations.

When the system parameters (including the delays) are constant and. Necessary and sufficient conditions guaranteeing the stability of the closed-loop system under the PPF are obtained in terms of the stability of a class of integral delay operators (systems).

Moreover, it is shown that the PPF can compensate arbitrarily large yet bounded input delays provided the open-loop (time-varying linear) system is only. Abstract: In this paper we extend the finite-time stability (FTS) theory to two dimensional (2D)-systems.

Such class of systems plays an important role in many engineering contexts, such as digital filtering, image processing, gas absorpsion technology, as well as in other fields, like seismological data processing, thermal and industrial processes. Studying the stability of dynamic systems is critical, but analyzing the stability of time-delay systems is challenging because DDEs are infinite-dimensional.

We propose a new approach to quickly generate stability charts for DDEs using continuation of characteristic roots (CCR). nite-time stability and finite-time stabilization for a class of linear time-delay systems.

To the best of the authors’ knowledge, a little work has been done for the finite-time stability and stabilization of time-delay systems. Some early results on finite time stability of time-delay systems.

This paper is concerned with systems of functional differential equations with either finite or infinite delay. We give conditions on the system and on a Liapunov function to ensure that the zero solution is asymptotically stable. Section 2 is devoted to finite delay, Section 3 to infinite delay.

Abstract. In this paper, exponential stability and robust control problem are investigated for a class of discrete-time time-delay stochastic systems with infinite Markov jump and multiplicative noises.

The jumping parameters are modeled as an infinite-state Markov chain. By using a novel Lyapunov-Krasovskii functional, a new sufficient condition in terms of matrix inequalities is derived to.

Based on the theories of fractional differential equations, we obtain three theorems on the finite-time stability, which give some sufficient conditions on finite-time stability, respectively, for homogeneous systems without and with time delay and for the nonhomogeneous system with time delay.

Finite-Time Stability of Uncertain Nonlinear Systems with stability, which is defined over an infinite time interval [16–18]. However, in practice, it is more meaningful to Section 2, the model of uncertain nonlinear systems with time-varying delay and external disturbances is presented.

Abstract: In this brief, we propose an approach based on the Laplace transform and “inf-sup” method for studying finite-time stability of fractional-order systems (FOS) with time-varying delay and nonlinear perturbation.

Based on the proposed approach, we establish new delay-dependent conditions for finite-time stability of FOS with interval time-varying delay.

The aim of this paper is to establish stability criteria for impulsive control systems with finite and infinite delays by employing the largest and smallest eigenvalue matrix. Inspired by the idea in dealing with impulsive control systems, some stability criteria are established.

The rest of this paper is organized as follows. In mathematics, delay differential equations (DDEs) are a type of differential equation in which the derivative of the unknown function at a certain time is given in terms of the values of the function at previous times.

DDEs are also called time-delay systems, systems with aftereffect or dead-time, hereditary systems, equations with deviating argument, or differential-difference equations. Finite Dimensional State Representation of Linear and Nonlinear Delay Systems Odo Diekmann Department of Mathematics, University of Utrecht, P.O.

BoxTA Utrecht, The Netherlands of the delay system can be obtained from the solutions of a nite system of ordinary di erential equations. For linear autonomous systems and linear sys. The book is a collection of tools and techniques that make predictor feedback ideas applicable to nonlinear systems, systems modeled by PDEs, systems with highly uncertain or completely unknown input/output delays, and systems whose actuator or sensor dynamics are modeled by more general hyperbolic or parabolic PDEs, rather than by pure delay.

Delay Compensation for Nonlinear, Adaptive, and PDE Systems is an excellent reference for graduate students, researchers, and practitioners in mathematics, systems control, as well as chemical, mechanical, electrical, computer, aerospace, and civil/structural engineering.

Parts of the book may be used in graduate courses on general distributed. Review of the Finite Element Method (FEM) FEM: Numerical Technique for approximating the solution of continuous systems.

The MFE is based on the physical discretization of the observed domain, thus reducing the number of the degrees of freedom; and shifting from an analytical to a numerical formulation. Continuous Discrete. A H ∞ filter model is constructed to solve the issue of state estimation for the Hamiltonian systems with time varying delay in the state.

Some sufficient conditions are proposed to obtain effective filter gain and achieve the H ∞ performance for the augmented system consisted of the Hamiltonian system and the filter.

Simulation results. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, \', () Survey of the Stability of Linear Finite Difference Equations* P. LAX and R. RICHTMYEK PART I AN EQUIVALENCE THEOREM 1. Introduction Beginning with the discovery by Courant, Friedrichs and Lewy [l] of the conditional stability of certain finite difference approximations to.

The design and analysis of the adaptive predictors involves a Lyapunov stability study of systems whose dimension is infinite, because of the delays, and nonlinear, because of the parameter estimators.

This comprehensive book solves adaptive delay compensation problems for systems with single and multiple inputs/outputs, unknown and distinct. Keywords: controllability, delay systems, δ-freeness, distributed delays, infinite dimensional systems, quasi-finite systems, spectral controllability, tracking.

Contents 1. Introduction 2. Examples of Delay Systems Derived from Distributed Parameter Systems 3.

Controllability Notions for Linear Delay Systems Various approaches We consider the question of when delay systems, which are intrinsically infinite dimensional, can be represented by finite dimensional systems.

Specifically, we give conditions for when all the information about the solutions of the delay system can be obtained from the solutions of a finite system of ordinary differential equations. For a finite ensemble, we can model the dynamics of the Kuramoto ensemble by the stochastic Kuramoto system with multiplicative noise.

In contrast, for an infinite ensemble, the dynamics is effectively described by the Kuramoto-Sakaguchi-Fokker-Planck(KS-FP) equation with state dependent degenerate diffusion. The authors in have derived the delay-independent robust H ∞ stability criteria for discrete-time T-S fuzzy systems with infinite-distributed delays.

Recently, many robust fuzzy control strategies have been proposed a class of nonlinear discrete-time systems with time-varying delay and disturbance [ 15 - 33 ].

The Markov chain approximation methods are widely used for the numerical solution of nonlinear stochastic control problems in continuous time. This book extends the methods to stochastic systems with delays.

Because such problems are infinite-dimensional, many .