I-Kong Fong

Stability analysis of linear systems with time delay

This paper presents asymptotic stability criteria for linear systems with time delay. The results not only improve previous results, but also provide a bound for the delay time such that if the system is asymptotically stable when the delay does not exist, it retains the asymptotic stability when the delay time is within the bound. >

Dynamic interval systems analysis and design

In this paper, new sufficient conditions for the stability of interval matrices are presented. Subsequently, design procedures are provided to synthesize robust static feedback controllers for dynamic interval systems. Both optimal control and pole region assignment design techniques are applied to make the closed-loop system achieve the requirements in system performance and stability robustness. Examples given confirm the availability of the proposed design approaches.

Robust stability analysis of linear continuous/discrete-time systems with output feedback controllers

The robust stability of linear systems with output feedback controllers and time-varying uncertain parameters is considered. The robust stability bounds for time-varying uncertain parameters are given using the Lyapunov method. When there are no uncertain parameters in the input and/or output matrices, it is shown that the result for continuous-time systems is the same as that presented by K.M. Zhou and P.P. Khargonekar (1987), and the result for discrete-time systems is better than that of S.R. Kolla (1989) for the same example. >

New robust stability bounds of linear discrete-time systems with time-varying uncertainties

This paper presents new uncertain parameter variation bounds for linear discrete-time systems to preserve asymptotic stability. The Lyapunov method is utilized to treat both structured and unstructured uncertainties, and the results are optimized with respect to a parameter in the inequality used. When applied to examples considered by previous authors, our results give less conservative bounds.

A real-time equipment monitoring and fault detection system

In semiconductor fabrication processes, real-time equipment monitoring and fault detection become critical as most problems reveal themselves first on the equipment performance and much later on the wafer quality. The sooner we can detect the problem, the lower the production loss. The goal of this paper is to present an integrated equipment monitoring approach for a PECVD tool. The approach will include: (1) simultaneous monitoring scheme: a dartboard display of real-time data that provides an easy reading of the equipments overall status, (2) system health index: an index that evaluates the equipments overall health, and (3) analysis functions that include various charting functions, real-time SPC, run-to-run SPC, and other advanced SPC functions. The system has been implemented in TSMC FAB IV for testing. The preliminary results show that the proposed system is an effective tool for real-time monitoring and fault detection.

Analysis and applications of robust nonsingularity problem using the structured singular value

This note uses the structured singular value technique to solve the robust nonsingularity analysis problem for matrices with unstructured and/or quadratically coupled structured uncertainties. With the ready /spl mu/-analysis tools, a new approach is proposed for finding a set of uncertainties within which the perturbed matrix keeps nonsingularity. Applications and examples in robust control theory are given to show the usefulness and the practicality of the proposed approach. >

Stability of perturbed polynomials based on the argument principle and Nyquist criterion

The stability robustness of the characteristic polynomial with perturbed coefficients for linear time-invariant systems is studied. The Schur, strictly Hurwitz, and G-stability properties of perturbed polynomials are all considered with a unified approach. New upper bounds on the allowable coefficient perturbation of a polynomial, for keeping one of the stability properties, are obtained. The proposed upper bounds are directly formulated in terms of the polynomial coefficients and can be computed easily. We also provide a sufficient condition for the discrete stability of interval polynomials and an algorithm for testing the G-stability of polynomials with constant coefficients. Illustrative examples are given to show the applicability of our results, especially in determining measures of stability robustness for any Schur polynomial subject to coefficient perturbation.

Comments on "Discrete optimal control with eigenvalue assigned inside a circular region

The commenters claim that the perturbation bound for the stability of a linear optimal system derived in the paper by T.T. Lee et al. (see ibid., vol.AC-31, p.958-62 (1986)) is incorrect. The source of the error is identified and a corrected result is given. Furthermore, it is pointed out that an even more fundamental problem exists before the derivation process is started. A remedy is suggested. >

Rank preservation of matrices with structured uncertainties and its applications in robust control theory

Matrix rank is determined by the nonsingularity of its submatrices. For matrices in which entries are quadratic functions of some uncertain parameters, this paper derives sufficient conditions on parameters to that ensure the matrices preserve to some degrees the ranks they have when the parameters are all zero. The rank preservation problem is converted to the nonsingularity analysis problem of the minors of the matrix in discussion, and suitable tools such as the /spl mu/-analysis method are used to solve the problem. Applications in robust control theory, including tests for robust controllability/observability, minimum phaseness, coprimeness, and Schur stability, are given, together with illustrative examples,. >

Stability analysis of systems with commensurate time delays

Presents a computationally tractable method for checking whether a linear system with commensurate time delays is stable independently of delay. The method needs only finite computations, and is stronger than previous results which are only sufficient conditions. The method involves only eigenvalue calculations of some matrices to verify the necessary and sufficient condition. The robust delay-independent stability of such systems is discussed when there are uncertain parameters.<<ETX>>