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Page 4669 of Mathematical Reviews Vol. , Issue 91H [page]

1991 Mathematical Reviews  
The authors consider the robust Schur stability of a family of complex polynomials whose coefficients are defined in terms of a diamond.  ...  The robust stability condition given for this family involves testing the Schur stability of eight particular edges of the polynomial family.  ... 

On Stability of Parametrized Families of Polynomials and Matrices

Handan Akyar, Taner Büyükköroğlu, Vakıf Dzhafarov
2010 Abstract and Applied Analysis  
The Schur and Hurwitz stability problems for a parametric polynomial family as well as the Schur stability problem for a compact set of real matrix family are considered.  ...  It is established that the Schur stability of a family of real matrices is equivalent to the nonsingularity of the family if has at least one stable member.  ...  Acknowledgment The authors would like to thank the reviewers for their helpful suggestions to the improvement of this paper.  ... 
doi:10.1155/2010/687951 fatcat:nkf3chjyqfgh7lzoualuwcs4sa

Page 6861 of Mathematical Reviews Vol. , Issue 94k [page]

1994 Mathematical Reviews  
Summary: “In this paper, we discuss the robust stability of a class of polynomial families more general than the interval polynomial family and diamond polynomial family.  ...  a class of polynomial families.  ... 

Robust Stability in Discrete Control Systems via Linear Controllers with Single and Delayed Time

B. L. Hernández-Galván, J. A. López-Rentería, B. Aguirre-Hernández, G. Fernández-Anaya
2018 Mathematical Problems in Engineering  
A polynomial approach technique to compute the maximal robust stability interval of the monoparametric system with single and delayed time controller is developed by using the zero exclusion principle  ...  In this work, a discrete feedback of single and a delayed time is introduced in a LTI control discrete system, yielding a monoparametric family of LTI systems.  ...  Acknowledgments The first author is supported by CONACYT as a Ph.D. fellowship and second author as CONACYT chair professor.  ... 
doi:10.1155/2018/3674628 fatcat:b3helyznrjdgraepe5iyzn3lqa

Page 576 of Mathematical Reviews Vol. , Issue 94a [page]

1994 Mathematical Reviews  
; (2) the Schur stability of interval polynomials and the robust stable degree for a Schur polynomial; (3) the Hurwitz stability of interval matrices and the robust stable degree of a Hurwitz matrix; (  ...  4) the Schur stability of interval matrices and the robust stable degree of a Schur matrix; (5) the robust stability of uncertain delay systems and control systems.” 94a:93057 93D09 Neimark, Yu.  ... 

Page 3509 of Mathematical Reviews Vol. , Issue 91F [page]

1991 Mathematical Reviews  
[Dahleh, Mohammed A.j} (1-TXAM-E) Robust stability of a family of disc polynomials. Internat. J. Control 51 (1990), no. 6, 1353-1362.  ...  Summary: “This paper gives necessary and sufficient conditions for robust stability of a family of polynomials F described as fol- lows: each polynomial P(s) in 7 is of the form P(s) = U(s)V(s)+ X(s)Y(  ... 

On the stability hyperellipsoid of a Schur polynomial

Q.-H. Wu, M. Mansour
1994 Linear Algebra and its Applications  
The robust Schur stability of a polynomial with uncertain coefficients is investigated. Using a linear fractional transformation, the stability hyperellipsoid of a Schur polynomial is determined.  ...  An effective algorithm is supplied for finding an optimal transformation parameter /3 such that the resulting stability hyperellipsoid encloses entirely the largest hypersphere.  ...  The bilinear transformation maps a Schur polynomial of degree n to a Schur polynomial of degree n. Proof.  ... 
doi:10.1016/0024-3795(94)90387-5 fatcat:dxgmq4iijjfrbgc2pttjhqedyi

Page 849 of Mathematical Reviews Vol. , Issue 2000a [page]

2000 Mathematical Reviews  
Finally, we give a result about preservation of stabilization and robust stabilization.” 2000a:93074 93D09 Garloff, Jiirgen; Graf, Birgit Robust Schur stability of polynomials with polynomial parameter  ...  An edge theorem for a polytopic family of multivariate polynomials and a stability theorem for in- terval polynomials as well as for a diamond family of multivariate polynomials are established which are  ... 

Page 3216 of Mathematical Reviews Vol. , Issue 96e [page]

1996 Mathematical Reviews  
and stability analysis of polynomial families.  ...  Summary: “A method is proposed to quickly calculate a lower bound for the size of stability-preserving perturbations in the coefficients of real Schur polynomials.  ... 

Page 4187 of Mathematical Reviews Vol. , Issue 89G [page]

1989 Mathematical Reviews  
Summary: “A new two-dimensional stability test is proposed, based on the stability robustness analysis of a relevant 1-D system family.  ...  The objective of this paper is to obtain conditions for robustness of low-order “Schur polynomials”.  ... 

Page 6008 of Mathematical Reviews Vol. , Issue 2001H [page]

2001 Mathematical Reviews  
Finally he calculates the robust stability radius for a spherical family of multivariate polynomi- als.  ...  The paper deals with the robust stability of 2D discrete-time linear time-invariant systems via the investigation of the robust stabil- ity for two-variable Schur polynomials.  ... 

Common diagonal solutions to the Lyapunov inequalities for interval systems

Bengi Yıldız, Taner Büyükköroğlu, Vakif Dzhafarov
2016 Journal of Inequalities and Applications  
In the general case a sufficient condition is obtained for a common diagonal solution in terms of the center and upper bound matrices of an interval family.  ...  For third order systems, an algorithm for the evaluation of common solutions in the case of existence is given.  ...  The necessary condition for the existence of a common diagonal solution is the robust diagonal stability, that is, diagonal stability of each matrix from the family A.  ... 
doi:10.1186/s13660-016-1194-x fatcat:4ubizc4yzbalrix36dl7ysypae

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

1994 Mathematical Reviews  
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  ...  Summary: “A controller stabilizes an entire interval plant family if it simultaneously stabilizes sixty-four polynomials.” 94b:93106 93D09 34D10 34H05 93B35 Foo, Y. K.  ... 

Page 3954 of Mathematical Reviews Vol. , Issue 2003e [page]

2003 Mathematical Reviews  
It is shown that 2- D scattering Schur polynomials of specified partial degrees can be covered by the model and some parameter sets lead to polynomials which are Schur in a broad sense.  ...  At the end of the paper two test examples are presented: robust control of a flexible actuator and robust autopilot of a missile.  ... 


Yang Xiao
2008 Asian journal of control  
The stability of 2-D s-z vertex polynomials and 2-D s-z edge polynomials were tested by using a Schur Table of complex polynomials.  ...  Determining the robust stability of interval quasipolynomials leads to a NP problem: an enormous number of testing edge polynomials.  ...  It is easy to see that the coefficients in Eq. (12) satisfy Thus, we can derive an edge test for the robust Hurwitz-Schur stability of interval bivariate polynomials.  ... 
doi:10.1111/j.1934-6093.2006.tb00267.x fatcat:52izcldmvjalja4ffuedy37d2u
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