Showing papers by "Jie Chen published in 2007"

The Final Value Theorem Revisited - Infinite Limits and Irrational Functions

Abstract: The aim of this article is to publicize and prove the ";infinite-limit"; version of the final value theorem. The version we provide is a slight refinement of the classical literature in that we require that s approach zero through the right-half plane to obtain the correct sign of the infinite limit. We first consider the case of rational Laplace transforms and then state a version that applies to irrational functions. For rational Laplace transforms with poles in the OLHP or at the origin, the extended final value theorem provides the correct infinite limit. For irrational Laplace transforms, the generalized final value theorem provides the analogous result. Finally, we point to a detailed analysis of the final value theorem for piecewise continuous functions.

High-Order Analysis Of Critical Stability Properties of Linear Time-Delay Systems

Abstract: In this paper we study stability properties of linear time-delay systems with commensurate delays. We investigate specifically the asymptotic behavior of the critical characteristic zeros of time-delay systems on the imaginary axis. This behavior determines whether the imaginary zeros cross from one half plane into another, and hence plays a critical role in determining the stability of a time-delay system. We emphasize in particular the second-order asymptotic properties, which, together with earlier results on first-order analysis, provide a more complete characterization of the zero asymptotic behavior.

What Is Your Favorite Book on Classical Control? Responses to an Informal Survey

Abstract: Champaign. His research interests focus on mathematical control theory, distributed motion coordination for groups of autonomous agents, and geometric mechanics and geometric integration. He is the author of Geometric , Control and Numerical Aspects of Nonholonomic Systems (Springer Ver-lag, 2002). William B. Dunbar (unbar@soe.ucsc. edu) earned a B.S. degree in engineering science and mechanics from Vir-ginia Tech in 1997, an M.S. degree in applied mechanics and engineering science from UC San Diego in 1999, and a Ph.D. in control and dynamical systems from Caltech in 2004. He is currently an assistant professor in the Department of Computer Engineering at UC Santa Cruz. His research areas include distributed model predictive control, air traffic control, and applications of control to problems in biophysics and sequencing. A s part of this special section on classical control, we asked control experts in academia and industry about their favorite textbook on classical control. The survey was informal and not meant for statistical purposes, but it did result in some interesting replies. Due to the large number of responses, not all are included here, and many responses have been edited for length. If you did not contribute to this survey, we invite your responses for a follow-up article. Interesting and memorable stories about your favorite classical control textbook, course, or instructor are most welcome. Not surprisingly, many responses refer to textbooks that have been around for decades but are still in print. Some favor the textbook written originally by Dorf and now co-authored with Bishop: » I have used the textbooks by the following authors over the past 20 years: Dorf and Nise. Each has strengths and weaknesses. However, among all of them, I prefer the first one. My main reasons are as follows: The book covers the control topics in a logical fashion ; each chapter explains the subject in a simple way; the derivations of the formulas are complete and convince the students ; tables, figures, and illustrations are excellent and useful for better understanding of the subjects; the numerous examples and problems represent all fields; the book shows the students the applicability of control systems to many facets of real life. The book makes the students aware that control systems are multidisciplinary. The modeling of many diverse systems taken from different applications are either derived or referenced for further investigation. This approach makes it easy for the students to realize that real systems …

When will zeros of time-delay systems cross imaginary axis?

Abstract: A time-delay system may or may not be stable for different periods of delay When will then a delay system be stable or unstable, and for what ranges of delay? This paper attempts to answer these questions We show that by finding a set of critical delay values, for which the system's characteristic quasipolynomial has zeros on the imaginary axis, it is possible to determine its stability in the full range of the delay parameter by characterizing the analytical behaviors of the zeros This characterization is facilitated by an operator perturbation approach, which is both conceptually attractive and computationally efficient The entire procedure, which first identifies the critical zeros on the imaginary axis and next determines whether the zeros cross the imaginary axis, requires only solving a generalized eigenvalue problem

Computing maximum delay deviation allowed to retain stability in systems with two delays

Abstract: This chapter discusses the calculation of maximum delay deviation without losing stability for systems with two delays. This work is based on our previous work on the properties of the stability crossing curves in the delay parameter space. Based on the results, an algorithm to calculate the maximum radius of delay deviation without changing the number of right hand zeros of the characteristic quasipolynomial can be devised. If the nominal system is stable, then the system remains stable when the delays do not deviate more than this radius.

An alternative characterization of robust stability and stability radius for linear time delay systems

Abstract: This paper considers the problems of robust stability and stability radius pertaining to certain linear time delay systems. The aim is to establish the connection between recently published results on robust stability of time-delay systems based on matrix inequalities and computation of stability radius. As a result of this connection, an alternative formula to compute the real stability radius of time-delay systems with structured uncertainties is provided. We also report on explicit formulas for stability radius of special classes of time-delay systems.

On the robust stability of some parameter-dependent linear systems: solutions via matrix pencil techniques

Abstract: This note focuses on deriving stability conditions for a class of linear parameter-dependent systems in a state-space representation. More precisely, we will compute the set of parameters for which the characteristic roots are located on the imaginary axis, and next we will give the characterization of the way such critical roots are crossing the imaginary axis. The methodology considered makes use of the computation of the generalized eigenvalues of an appropriate matrix pencil combined with an operator perturbation approach for deriving the crossing direction. Finally, the particular case of parameter-dependent polynomials will be also considered, and the stability analysis of time-delay systems is also revisited in this perspective.

Infinite Limits and Irrational Functions

Abstract: The final value theorem is an extremely handy result in Laplace transform theory. In many cases, such as in the analysis of proportional-integral-derivative (PID) controllers, it is necessary to determine the asymptotic value of a signal. The final value theorem provides an easy-to-use technique for determining this value without having to first invert the Laplace transform to determine the time signal. The standard assumptions for the final value theorem [1, p. 34] require that the Laplace transform have all of its poles either in the open-left-half plane (OLHP) or at the origin, with at most a single pole at the origin. In this case,