James A. Heinen

Sufficient conditions for stability of interval matrices

Extremely simple sufficient conditions are presented for the stability of interval matrices. These complement the necessary and sufficient conditions developed by Bialas (1983), which become unwieldy for large matrices (4×4 and above).

On algorithms for velocity estimation using discrete position encoders

Velocity information for a rotating device may be acquired via a discrete position encoder. The focus of this paper is on analyzing and improving the low speed and high acceleration accuracy of velocity measurements through the use of digital filters for control applications. The frequency-domain characteristics of various digital filters that may be used to estimate velocity from pulse-encoded velocity data are investigated and used to explain the performance of the digital filters in estimating velocity for a given velocity profile. A new digital filter design technique based on an adaptive least squares approach is presented in addition to several previously developed fixed-time velocity estimators. The performance characteristics of these velocity estimators are compared using pulse-encoded velocity data from an actual motor.

A simple algorithm for arbitrary polynomial transformation

A very simple algorithm is developed for the arbitrary rational transformation of a polynomial. The fact that many of the multiplications performed involve one zero factor is not explicitly taken into account. If desired, this could be done, with some increase in the complexity of the algorithm itself. Finally, if roundoff error is expected to be a problem, double precision arithmetic could be used. >

Further results concerning finite-time stability

Weiss and Infante [1], [2] developed sufficient conditions for finite-time stability of a vector differential equation. It is shown here that some of their theorems actually imply the stronger property of uniform finite-time stability. A theorem is presented which gives sufficient conditions for stability but not necessarily uniform stability. It is shown that this theorem can in certain cases yield better results than those of Weiss and Infantes corresponding theorem.

Set stability of differential equations

Abstract In recent years numerous definitions of stability having a more quantitative nature than most classical stability definitions have been presented by various investigators. These definitions involve known specific bounds on solutions of tho differential equation in question. In this paper a now type of stability (‘set stability’) is introduced which generalizes upon and in some respects unifies those recent endeavours in ‘ quantitative stability theory ’. The usual ‘Liapunov technique’ is employed in obtaining sufficient conditions for the various forms of set stability.

Evaluation of a technique involving processing with feature extraction to enhance the intelligibility of noise-corrupted speech

Results obtained in an experimental evaluation of speech intelligibility of an adaptive processing technique designed to enhance the intelligibility of speech in noise are presented. The technique relies on speech features extracted from noise-corrupted speech to control a cepstral processor. The speech-processing algorithm has been improved over the fundamental technique described by R.J. Conway and R.J. Niederjohn (1987). The evaluation method makes use of a computer implementation of a modified version of the diagnostic rhyme test. Results for four subject and several signal-to-noise ratios are presented.<<ETX>>

Comparison theorems for set stability of differential equations

Set stability and uniform set stability of differential equations involve known specific bounds on solutions of the differential equations under consideration. Comparison theorems are presented giving sufficient conditions for these forms of stability. The conditions include the existence of a Liapunov-Like function and the set stability of a scalar differential equation. Examples are given to demonstrate the method.

A technique for solving the extended Liapunov matrix equation

A technique for solving the extended Liapunov matrix equation is presented. The system matrix is first transformed to its Jordan canonical form. Then an explicit solution is obtained for the equivalent extended Liapunov matrix equation that results.

Lagrange stability and higher order derivatives of Liapunov functions

It is shown that the Lagrange stability of an autonomous system can be determined on the basis of the existence of a Liapunov function and the satisfaction of a certain inequality involving its first three derivatives.

Set stability of differential equations with time delay

Set stability and uniform set stability involve known specific bounds on the solutions of differential equations. These concepts are extended to include the case of differential equations with time delay. Liapunov-like theorems are presented which yield sufficient conditions for the set stability of such systems. Examples are given to demonstrate the method.