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1
Content available On the existence of a common solution to the Lyapunov equations
Białas S., Góra M.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2015
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Vol. 63, nr 1
163-–168
EN
In this paper, a system of Lyapunov equations A*i P + PAi = −Qi (i = 1, . . . ,m), (A) is considered in which Ai are given n × n complex matrices, Qi are unknown n × n Hermitian positive definite matrices and P, if any, is a common solution to the Lyapunov equations (A). Both sufficient and necessary and sufficient conditions are derived for the existence of such a matrix P. Examples are presented to illustrate the results.
2
Evaluation of surface morphology of texturized Si wafers for solar cells applications
Białas S.
Elektronika : konstrukcje, technologie, zastosowania
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2012
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Vol. 53, nr 6
94-97
PL
W pracy zbadano wpływ regularności ułożenia standardowej, piramidalnej tekstury, powstającej w wyniku anizotropowego trawienia krzemu w roztworach alkalicznych, na współczynniki odbicia światła. Przebadano dwa parametry: stopień pokrycia powierzchni teksturą i rozrzut wielkości piramid.
3
Content available remote Schur stability of the convex combination of complex polynomials
Białas S., Białas M.
Control and Cybernetics
|
2010
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Vol. 39, no 2
551-558
EN
This paper gives a necessary and sufficient condition for Schur stability of the convex combination of complex polynomials. It is a generalization of the work by Ackerman and Barmish (1988).
4
Content available remote An algorithm for the calculation of the minimal polynomial
Białas S., Białas M.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2008
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Vol. 56, nr 4
391-393
EN
This paper gives the simple algorithm for calculation of the degree and coefficients of the minimal polynomial for the complex matrix A = [aij ]n×n.
5
Content available remote New necessary conditions for optimal control of linear stationary systems
Białas S., Górecki H.
Archives of Control Sciences
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2007
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Vol. 17, no. 2
121-134
EN
The linear-quadratic problem in the system with proportional controllers is considered. New necessary conditions for establishing optimal values of gains Ki are determined which are very simple and convenient for calculations. New properties of the Hurwitz matrix are also discovered. The proposed method is alternative to the well known algebraic Riccati equations.
6
Content available A sufficient condition for Schur stability of the convex combination of the polynomials
Białas S.
Opuscula Mathematica
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2005
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Vol. 25, no. 1
25-28
EN
In this paper is given a simple sufficient condition for Schur stability of the convex combination of the real polynomials.
7
Content available A necessary and sufficient condition for sigma-Hurwitz stability of the convex combination of the polynomials
Białas S.
Opuscula Mathematica
|
2005
|
Vol. 25, no. 2
165-168
EN
In the paper are given a necessary and sufficent condition for sigma-Hurwitz stability of the convex combination of the polynomials.
8
Analiza strukturalna sprawdzianów szczękowych
Białas S., Humienny Z., Żach P.
Systems : journal of transdisciplinary systems science
|
2004
|
Vol. 9, No. sp. I
110-119
PL
Zagadnienia oceny sztywności sprawdzianów były do tej pory rozpatrywane najczęściej za pomocą, badań doświadczalnych. Wykorzystanie analizy numerycznej umożliwia przeanalizowanie zachodzących zjawisk już na etapie projektowania przyrządów. W referacie przedstawiono podstawy teoretyczne i wyniki analizy strukturalnej wykonanej przy zastosowaniu MES.
EN
Evaluation stiffness gauge problems were consider up to time by laboratory tests. Already on design stage used numerical analyses make possible effect proceed. In this paper we refer theoretical base and structural analyses result made by FEA.
9
Content available remote A sufficient condition for Hurwitz stability of the convex combination of two matrices
Białas S.
Control and Cybernetics
|
2004
|
Vol. 33, no 1
109-112
EN
The paper provides a simple sufficient condition for Hurwitz stability of the convex combination of two real matrices.
10
Content available remote A necessary and sufficient condition for stability of the convex combination of polynomials
Białas S.
Control and Cybernetics
|
2004
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Vol. 33, no 4
589-597
EN
This paper gives a necessary and sufficient condition for the Hurwitz (Schur) stability of the convex combination of the complex polynomials f1(x),f2(x),...,fm(x). It provides a generalization of the Ackermann, Barmish (1988). Barlett, Hollot, Huang (1988) and Bialas (1985).
11
Content available remote Tolerancje geometryczne w specyfikacji geometrii wyrobu
Białas S.
Mechanik
|
2003
|
R. 76, nr 3
140-144
EN
Geometrical tolerances describing in the complex way the permissible deviations from the geometrical form of a product (of a part or an assemby of a machine) in relation to the nominal form.
12
Content available remote Robust Stability of D-symmetrizable Hyperbolic Systems
Ziółko M., Białas S.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2001
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vol. 49, nr 1
167-176
EN
The systems under consideration are governed by a set of first-order linear partial differential hyperbolic equations together with boundary conditions. The Lyapunov method is used to verify the stability of the initial-boundary value problem. Necessary and sufficient conditions for stability are obtained under the assumption that the matrix coefficients in the differential equations and in the boundary conditions are D-symmetrizable. The considered systems have an interesting property: Hurwitz type stability and Schur type stability occur in one system simultaneously. The stability of the conditions type system is a stability of wave propagation. The stability of the discrete type system is a stability of the boundary feedback and the boundary reflections. Necessary and sufficient conditions for the robust stability of an initial-boundary value problem are obtained for the case where the matrix coefficients belong to a convex hull of stable and D-symmetrizable matrices.
13
Content available remote Necessary and Sufficient Conditions for the Stability of Interval Matrices
Białas S., Jakubowska M.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2001
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vol. 49, nr 3
467-477
EN
In this paper new necessary and sufficient conditions for the stability of the interval matrix [formula] are presented. These conditions represent a modification of paper [13]. Also, an algorithm for checking the stability of the interval matrix [formula] is proposed. The comparison of efficiency of the new algorithm and the algorithm from paper [13] is demostrated by means of examples.
14
Content available remote Necessary and Sufficient Conditions for Robust D-symmetrizability of Matrices
Białas S., Ziółko M.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2001
|
vol. 49, nr 1
177-182
EN
An algorithm for matrix D-symmetrizability verification is presented. Necessary and sufficient conditions for the D-symmetrizability of matrix convex combination are proved.
15
Content available remote Necessary and Sufficient Condition for the Hurwitz Stability of Symmetrizable Interval Matrices
Białas S.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2000
|
Vol. 48, nr 4
587-593
EN
This paper gives a necessary and sufficient condition for the Hurwitz stability of interval matrices [formulas], where [formula] are symmetrizable by the matrix [formula]. This result is a generalization of the papers [3], [4], where it was assumed that the matrices [formula] are symmetric.
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