Keqin Gu

An integral inequality in the stability problem of time-delay systems

An integral inequality is derived, and applied to the stability problem of time-delay systems using discretized Lyapunov functional formulation. As the result, a simpler stability criterion is derived.

Survey on Recent Results in the Stability and Control of Time-Delay Systems*

This paper gives a broad overview of the stability and control of time-delay systems. Emphasis is on the more recent progress and engineering applications. Examples of practical problems, mathematical descriptions, stability and performance analysis, and feedback control are discussed.

A further refinement of discretized Lyapunov functional method for the stability of time-delay systems

The discretized Lyapunov functional method for the stability problem of time-delay systems is further refined using a combination of integral inequality and variable elimination technique. As a result, the computational requirement is further reduced for the same discretization mesh. For systems without uncertainty, the convergence to the analytical solution is greatly accelerated. For uncertain systems, the new method is much less conservative. Numerical examples are presented to illustrate the effectiveness of the method.

Discretized LMI set in the stability problem of linear uncertain time-delay systems

The stability problem of linear uncertain time-delay systems is considered using a quadratic Lyapunov functional. The resulting stability criterion is a constrained linear matrix inequality set. The condition is necessary and sufficient if it is applied to uncertainty-free systems. A discretization scheme is proposed to reduce the constrained LMI set to a regular LMI problem. Conservatism due to discretization can be made small through finer discretization. Comparison with a previous example shows significant improvements even under very coarse discretization.

Advances in Time-Delay Systems

I Basic Theory.- Basic Theory for Linear Delay Equations.- II Stability and Robust Stability.- Complete Type Lyapunov-Krasovskii Functionals.- Robust Stability Conditio ns of Quasipolynomials by Frequency Sweeping.- Improvements on the Cluster Treatment of Characteristic Roots and the Case Studies.- From Lyapunov-Krasovskii Functionals for Delay-Independent Stability to LMI Conditions for -Ana1ysis.- III Control, Identification, and Observer Design.- Finite Eigenstructure Assignment for Input Delay Systems.- Control of Systems with Input Delay-An Elementary Approach.- On the Stabilization of Systems with Bounded and Delayed Input.- Identifiability and Identification of Linear Systems with Delays.- A Model Matching Solution of Robust Observer Design for Time-Delay Systems.- IV Computation, Software, and Implementation.- Adaptive Integration of Delay Differential Equations.- Software for Stability and Bifurcation Analysis of Delay Differential Equations and Applications to Stabilization.- Empirical Methods for Determining the Stability of Certain Linear Delay Systems.- Stability Exponent and Eigenvalue Abscissas by Way of the Imaginary Axis Eigenvalues.- The Effect of Approximating Distributed Delay Control Laws on Stability.- V Partial Differential Equations, Nonlinear and Neutral Systems.- Synchronization Through Boundary Interaction.- Output Regulation of Nonlinear Neutral Systems.- Robust Stability Analysis of Various Classes of Delay Systems.- On Strong Stability and Stabilizability of Linear Systems of Neutral Type.- Robust Delay Dependent Stability Analysis of Neutral Systems.- VI Applications.- On Delay-Based Linear Models and Robust Control of Cavity Flows.- Active-adaptive Control of Acoustic Resonances in Flows.- Robust Prediction-Dased Control for Unstable Delay Systems.- Robust Stability of Teleoperation Schemes SUbject to Constant and Time-Varying Communication Delays.- Bounded Control of Multiple-Delay Systems with Applications to ATM Networks.- Dynamic Time Delay Models for Load Balancing. Part I: Deterministic Models.- Dynamic Time Delay Models for lA>ad Balancing. Part II: A Stochastic Analysis of the Effect of Delay Uncertainty.- VII Miscellaneous Topics.- Asymptotic Properties of Stochastic Delay Systems.- Stability and Dissipativity Theory for Nonnegative and Compartmental Dynamical Systems with Time Delay.- List of Contributors.

Further remarks on additional dynamics in various model transformations of linear delay systems

This paper focuses on the analysis of conservatism introduced due to some model transformations used in the control literature. This work is an extension of a previous paper by the authors (1999) on additional dynamics. The additional dynamics of the second order and parametrized model transformations are examined. The neutral model transformation introduces additional constraints for stability, which can be analyzed in a very similar manner to additional dynamics.

H/sub /spl infin// control of systems under norm bounded uncertainties in all system matrices

This paper concerns H/sub /spl infin// control of systems under norm bounded uncertainties in all the system matrices. This is an extension of the work by Xie et al.(1992), where only the A matrix is allowed to be uncertain. It is found that the problem shares the same formulation with the H/sub /spl infin// control problem for systems without uncertainties. It can also be viewed as reducing the problem of dealing with systems with both structured uncertainties and unstructured uncertainties to one with unstructured uncertainties only. >

Discretized Lyapunov functional for systems with distributed delay and piecewise constant coefficients

The stability problem for systems with distributed delay is considered using discretized Lyapunov functional. The coefficients associated with the distributed delay are assumed to be piecewise constant, and the discretization mesh may be non-uniform. The resulting stability criteria are written in the form of linear matrix inequality. Numerical examples are also provided to illustrate the effectiveness of the method. The basic idea can be extended to a more general setting with more involved formulation.

On robust stability of time-delay systems with norm-bounded uncertainty

This paper considers the robust stability problem for a class of time-delay systems with norm-bounded, and possibly time-varying uncertainty. Based on the discretized Lyapunov functional approach, a stability criterion is derived. The time-delay is assumed constant and known. Numerical examples show that the results obtained by this new criterion significantly improve the estimate of the stability limit over some existing results in the literature.

Brief paper: Lyapunov-Krasovskii functional for uniform stability of coupled differential-functional equations

This article discusses the Lyapunov-Krasovskii functional approach for the stability problem of coupled differential-functional equations. Such systems include, as special cases, many types of time-delay systems, including the lossless propagation model, some neutral time-delay systems and singular time-delay systems. After the general stability theory, the special case of coupled differential-difference equations is discussed, and the necessity for the existence of quadratic Lyapunov-Krasovskii functional is established. Discretization is used to render the stability criterion to an LMI form.