ISSN:0020-7179    

DOI:10.1080/00207177708922299

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

An account of the life of the mathematician E. J. Routh (1831–1907) is given, and a list of his publications is added.

ISSN:0020-7179    

DOI:10.1080/00207177708922300

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

It is shown how all the elements in an arbitrary regular Routh array can be obtained from minors of suitably defined Bézoutian matrices.

ISSN:0020-7179    

DOI:10.1080/00207177708922301

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

ISSN:0020-7179    

DOI:10.1080/00207177708922302

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

Hermite's stability criterion of 1854 is proved using matrix algebra in a way which is much more direct than Hermite's own proof. A matrix algebraic interpretation of Hermite's original proof is also given. A by-product of the new proof is a. generalization of Orlando's formula, which relates the determinant of then×nHermite stability matrix to the roots of the underlying characteristic equation. Connections with Liapunov functions and other topics are pointed out.

ISSN:0020-7179    

DOI:10.1080/00207177708922303

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

For linear dynamical systems with constant coefficients, Routh gave a set of stability criteria in terms of the coefficients of (i) the characteristic equation and (ii) the equation with roots which are the sums of the characteristic roots taken in pairs. This set of criteria involves ½n(n+1) inequalities, wherenis the system order. The present paper investigates whether some of these inequalities ore redundant. Forn< 0 it is found that ½n(n−1) inequalities are indeed redundant, i.e. can be omitted, leaving a set ofnconditions which fire both necessary and sufficient for stability. Also, forngeneral, certain of the inequalities are shown to be non-redundant, i.e. they cannot be omitted without destroying the sufficiency of the criteria.

ISSN:0020-7179    

DOI:10.1080/00207177708922304

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

In this paper the bounded-input—bounded-output (BIBO) stability condition for a linear multivariable two-dimensional digital filter is defined and discussed

ISSN:0020-7179    

DOI:10.1080/00207177708922305

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

The paper considers the following question : Given a square, non-singular polynomial matrix C(s)how do we check, without evaluating the determinant, whether all the zeros of det C(s) are in the open left-half plane ?

ISSN:0020-7179    

DOI:10.1080/00207177708922306

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

This paper presents a technique of analysis, synthesis and optimization of stationary automatic control systems, which is based on the introduction of a concept of spectra, Problems of analytical equivalence of stability criteria of Routh, Hurwitz and Markov, of stability inversion algorithms for stationary systems, of generalized determinant stability indices and uniform stability margin in the senses of their criteria are considered, Integral stability criteria are formulated and some characteristics of the primary spectrumRn. which is uniquely related to the characteristic equation, are discussed, Finally, some properties are given of the integral quadratic measure used for solving the problem of performance inversion for stationary systems and for determining loci describing a continuum of quasioptimal stationary systems that are to meet given requirements concerning dynamical characteristics.

ISSN:0020-7179    

DOI:10.1080/00207177708922307

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

In the transform analysis of linear systems the two classical approaches use complex functions to study gain as a function of frequency (the Nyquist—Bode approach)and to study frequency as a function of gain (the Evans root locus approach)The central feature of any transform approach to the analysis of linear multivariable systems is the use of transfer-function matrices, and it. is the primary purpose of this paper to explain how the ideas of studying gain as a function of frequency, and frequency as a function of gain, can be extended to the multivariable case by associating with transfer-function matrices characteristic gain functions and characteristic frequency functions

ISSN:0020-7179    

DOI:10.1080/00207177708922308

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor