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This note is concerned with the stability problem of linear delay-differential systems of neutral type. A discretized Lyapunov functional approach is developed. The resulting stability criterion is formulated in the form of a linear matrix inequality. For nominal systems, the analytical results can be approached with fine discretization. Numerical examples show significant improvement over approaches in the literature. Index Terms--Linear matrix inequality (LMI), Lyapunov functional, stability, time-delay, uncertainty.

The robust stability problem of linear time-delay systems with norm-bounded uncertainty is further investigated by using a refined discretized Lyapunov functional approach. A new stability criterion is derived. The computational requirement is reduced for the same discretization mesh. 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. Index Terms--Linear matrix inequality (LMI), Lyapunov functional, stability, time-delay, uncertainty.

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. Keywords: Time Delay, Stability, Feedback Control Lyapunov-Krasovskii Functional Linear Matrix Inequality

In a recent paper, it was proved that the frequency response arc and the inner frequency response set associated with D-stable polynomial is convex. This note points out that clockwise property and positive curvature is sufficient for convexity based on a result in classical differential geometry and provides an alternative proof of the convexity based on curvature. It is felt that this line of proof may be more easily generalized to study the rational function cases.

The design of stabilizing linear output feedback control of uncertain systems is a computationally demanding optimization problem as local minima may exist which are distinct from the global minimum. However, in some special cases, quasiconvexity can be proven through a simple redefinition of variables and/or a reformulation of the problem in the dual form. Such special cases include state feedback control for both discrete and continuous time systems.

The stability of linear systems subject to possibly fast time-varying uncertainties is analyzed. A method is developed to compute the upper bound of uncertainty size allowed for retaining quadratic stability. The algorithm consists of a two-level optimization. The inner level of the algorithm consists of choosing an extremum among a finite number of values. It is proved that although the outer level of the algorithm is a nonconvex optimization problem, no local minimum distinct from the global minimum can exist. An illustrative example is presented.

This paper concerns [H.sub.[infinity]] control of systems under norm bounded uncertainties in all the system matrices. This is an extension of the work by Xie et al. where only the A matrix is allowed to be uncertain. It is found that the problem shares the same formulation with the [H.sub.[infinity]] 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.

This note 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. Index Terms--Linear matrix inequality (LMI), Lyapunov functional, stability, time-delay, uncertainty.

This note 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 ,same authors on additional dynamics. The additional dynamics of the second order and parameterized 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. Index Terms--Delay, model transformation, stability.

In studying the stability of time delay systems, many published results use a transformation to transform a system with single time delay to a system with distributed delay. In this article, the inherent limitations of such approaches are studied. Specifically, it is shown that such a transformation incurs additional dynamics that can be characterized by appropriate additional eigenvalues. The critical delay values when such additional eigenvalues cross the imaginary axis can be explicitly calculated. If the smallest of such delays is less than the stability delay limit of the original system, then any stability criteria obtained using such transformation will be conservative. Some examples are also included. Index Terms--Razumikhin theorem, stability, time-delay systems.