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Page 5527 of Mathematical Reviews Vol. , Issue 94i [page]

1994 Mathematical Reviews  
The authors deal with Hurwitz stability of real polynomials whose coefficients belong to a diamond.  ...  Routh scheme and in terms of the determinants of the corresponding Hurwitz matrix.”  ... 

Page 382 of Mathematical Reviews Vol. , Issue 85a [page]

1985 Mathematical Reviews  
Authors’ summary: “A Routh-Hurwitz type test is given for asymptotic stability independent of delay for systems with com- mensurate time delays, and such a test for determining the in- tervals of the values  ...  Authors’ summary: “The task of checking that the zeros of a prescribed real exponential polynomial all have negative real part arises in examining the stability of delay-differential systems.  ... 

Maximal unidirectional perturbation bounds for stability of polynomials and matrices

Minyue Fu, B. Ross Barmish
1988 Systems & control letters (Print)  
Given a stable polynomial or matrix, we consider a class of umdirectional perturbations. In this note, we provide a closed form for the maximal perturbation bounds under which stability is preserved.  ...  The results are then used to derive a closed form for the maximal stability box around the coefficients of a nominally stable polynomial.  ...  Kehui Wei for discussion of the proof of Theorem 3.2.  ... 
doi:10.1016/0167-6911(88)90056-4 fatcat:46hq57adxvdehozzlihsatu5ea

Page 3119 of Mathematical Reviews Vol. , Issue 90E [page]

1990 Mathematical Reviews  
The paper gives various applications of the criteria of Routh, Hurwitz, and Hermite, as 93D Stability 90e:93087 well as the Hurwitz criterion for the case of complex coefficients.  ...  The paper is a survey on the Hurwitz criterion for the stability of polynomials with some new aspects related with Schur’s de- composition theorem for polynomials.  ... 

Page 1169 of Mathematical Reviews Vol. , Issue 94b [page]

1994 Mathematical Reviews  
Summary: “A Hurwitz stability criterion for the convex hull of two matrices due to C. R.  ...  Assume that a characteristic polynomial of a family of linear continuous-time systems is G(s) = Fi(s)P(s) + Fo(s)P(s), where F;(s), F)(s) are fixed polynomials and P;(s), P)(s) are in- terval polynomials  ... 

Page 7185 of Mathematical Reviews Vol. , Issue 89M [page]

1989 Mathematical Reviews  
A perturbation approach is presented to verify the stability of an interval matrix. (An interval matrix is a matrix whose entries belong to specified closed intervals of the real line.)  ...  In terms of algebraic criteria, the classical Routh- Hurwitz criterion gives a quite complete solution.  ... 

Stability and Multiscroll Attractors of Control Systems via the Abscissa

Edgar-Cristian Díaz-González, Baltazar Aguirre-Hernández, Jorge Antonio López-Rentería, Eric Campos-Cantón, Carlos Arturo Loredo-Villalobos
2017 Mathematical Problems in Engineering  
The results are extended in a straightforward way to interval polynomials; then we apply the abscissa as a measure to destabilize Hurwitz polynomial for the generation of a family of multiscroll attractors  ...  First we present some results about the abscissa of stability of characteristic polynomials from linear differential equations systems; that is, we consider Hurwitz polynomials.  ...  Jorge Antonio López-Rentería also wishes to thank CONACYT for the postdoctoral grant (Grant no. 290941-UIA) and the Iberoamerican University for the support in the realization of this paper. C. A.  ... 
doi:10.1155/2017/6743734 fatcat:bapks4wma5bknj6tlzxxupggxy

Page 1177 of Mathematical Reviews Vol. , Issue 93b [page]

1993 Mathematical Reviews  
A new family of metrics, called pointwise gap metrics, in the space of real rational matrices, is introduced.  ...  L. (1-WI-E) An approach to robust stability of matrix polytopes through copositive homogeneous polynomials. IEEE Trans. Automat. Control 37 (1992), no. 6, 848-852.  ... 

Stable Factorization of Strictly Hurwitz Polynomials

Ömer Eğecioğlu, B. Siddik Yarman
2010 International Journal of Computers Communications & Control  
We propose a stable factorization procedure to generate a strictly Hurwitz polynomial from a given strictly positive even polynomial.  ...  It is hoped that this factorization technique will provide a motivation to perform the factorization of two-variable positive function to generate scattering Hurwitz polynomials in two variables for which  ...  Basic elements of Routh-Hurwitz stability The conditions for a real polynomial g(z) = g 0 + g 1 z + g 2 z 2 + · · · + g n z n (6) with g 0 > 0 to be strictly Hurwitz are given in terms of the positivity  ... 
doi:10.15837/ijccc.2010.5.2229 fatcat:aprptcqoibg25iwh73onbpwbke

Probabilistic solutions to some NP-hard matrix problems

M. Vidyasagar, Vincent D. Blondel
2001 Automatica  
In this paper, we use standard bounds on empirical probabilities as well as recent results from statistical learning theory on the VC-dimension of families of sets de"ned by a "nite number of polynomial  ...  Abstract During recent years, it has been shown that a number of problems in matrix theory are NP-hard, including robust nonsingularity, robust stability, robust positive semide"niteness, robust bounded  ...  Let us begin by recalling the Hurwitz stability test for the stability of a polynomial, which is equivalent to the Routh test that is more familiar to control engineers (and which is almost universally  ... 
doi:10.1016/s0005-1098(01)00089-9 fatcat:p2b25gdvvrfyjjmomjv5gjjafm

Page 1525 of Mathematical Reviews Vol. , Issue 2003B [page]

2003 Mathematical Reviews  
The method consists in constructing a parametric Routh-like array with polynomial entries and generating Sturm se- quences for checking the absence of zeros of two real A-polynomials of degrees 2 and 2n  ...  of a rigid body with a fixed point.” 2003b:93063 93D09 93840 93D05 Yang, Shih-Feng ; Hwang, Chyi (RC-CHNG-KE; Chia-Yi) A test for robust Hurwitz stability of convex combinations of complex polynomials  ... 

A Panoramic Sketch about the Robust Stability of Time-Delay Systems and Its Applications

Baltazar Aguirre-Hernández, Raúl Villafuerte-Segura, Alberto Luviano-Juárez, Carlos Arturo Loredo-Villalobos, Edgar Cristian Díaz-González
2020 Complexity  
This paper presents a brief review on the current applications and perspectives on the stability of complex dynamical systems, with an emphasis on three main classes of systems such as delay-free systems  ...  Besides, criteria on robust stability and stability of nonlinear time-delay systems are presented, including some numerical approaches.  ...  Acknowledgments In memory of Oscar Villafuerte-Segura, my brother, my partner, and unconditional friend.  ... 
doi:10.1155/2020/9410315 fatcat:reyl2q3j7faghnfrpcc5dibyti

Design Of A Reduced Order Robust Convex Controller For Flight Control System

S. Swain, P. S. Khuntia
2014 Zenodo  
is tested graphically by using Kharitonov rectangle and Zero Exclusion Principle for a particular range of perturbation value.  ...  Then the order of the system model is reduced to a low-dimensional state space by using Balanced Truncation Model Reduction Technique and finally the robust stability of the reduced model of the system  ...  If the perturbation is further allowed beyond the above value of ' ' μ the polynomials are found not to be Hurwitz resulting the coefficients to be negative.  ... 
doi:10.5281/zenodo.1092150 fatcat:64s3zrlfkrcajnjdcqcjawdxyi

The problem of generalized D-stability in unbounded LMI regions [article]

Olga Y. Kushel, Raffaella Pavani
2020 arXiv   pre-print
For this, we consider a family of unbounded regions defined in terms of Linear Matrix Inequalities (so-called LMI regions).  ...  We study the problem when the localization of a matrix spectrum in an unbounded LMI region is preserved under specific multiplicative and additive perturbations of the initial matrix.  ...  We note that [34] provides necessary and sufficient conditions for the multiplicative D-stability of a 4 × 4 matrix resorting to the Routh-Hurwitz criterion, but the method appears too complicated to  ... 
arXiv:2004.11172v1 fatcat:ytqxtyiaxracrnzc27co2xwxpa

Stability of Fractional Order Systems

Margarita Rivero, Sergei V. Rogosin, José A. Tenreiro Machado, Juan J. Trujillo
2013 Mathematical Problems in Engineering  
Dynamical systems and control are one of the most active areas, and several authors focused on the stability of fractional order systems.  ...  Nevertheless, due to the multitude of efforts in a short period of time, contributions are scattered along the literature, and it becomes difficult for researchers to have a complete and systematic picture  ...  The work was done in the framework of cooperation between Belarusian State University and University La Laguna. The work is partly supported by Project MTM2010-16499 from the Government of Spain.  ... 
doi:10.1155/2013/356215 fatcat:ddc3x2xsszg3di2oqdjr5i4cye
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