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1
Content available Invariant properties of positive linear electrical circuits
100%
Kaczorek T.
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tom Vol. 68, nr 4
875--890
EN
The invariant properties of the stability, reachability, observability and transfer matrices of positive linear electrical circuits with integer and fractional orders are investigated. It is shown that the stability, reachability, observability and transfer matrix of positive linear systems are invariant under their integer and fractional orders.
2
Content available Designing of quasi one-dimensional acoustic filters using genetic algorithm
86%
Garus S. , Sochacki W.
Vibrations in Physical Systems
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2019
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tom Vol. 30, nr 2
art. no. 2019210
EN
In phononic quasi one-dimensional structures, there is a phenomenon of a phononic bandgap (PhBG), which means that waves of a given frequency do not propagate in the structure. The location and size of PhBG depend on the thickness of the layers, the type of materials used and their distribution in space. The theoretical study examined the transmission properties of quasi one-dimensional structures designed using a genetic algorithm (GA). The objective function minimized the transmission integral and integral of the absolute value of the transmission functions derivative (to eliminate high transmission peaks with a small half width) in a given frequency range. The paper shows the minimization of transmission in various frequency bands for a 40-layer structure. The distribution of multilayer structure transmission was obtained through the Transfer Matrix Method (TMM) algorithm. Structures surrounded by water were analyzed and built of layers of glass and epoxy resin.
3
Content available remote Exact solution to the structural instability of a parallel array of mutually attracting identical simply-supported plates
86%
Wang X. , Liu L.
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tom Vol. 69, nr 3
243--256
EN
By means of the theory of elasticity, we investigate the structural instability of a parallel array of identical simply-supported plates. One plate interacts with the neighboring plates through surface attractive forces. The proposed method is based on the 2 × 2 transfer matrix for a plate and on the solution of the generalized eigenvalue problem for the plate array. Analytical expressions of the critical interaction coefficients for two, three and four interacting plates are obtained when the end-effect of the plates at the ends of the parallel array and the surface energy of the plates are ignored. The influence of the end-effect and surface energy on the critical interaction coefficient is also numerically studied. Our solution is valid whether the plates are thin or extremely thick.
4
Content available Invariant properties of positive linear electrical circuits
86%
Kaczorek T.
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tom No. 97
109--123
EN
The invariant properties of the stability, reachability, and transfer matrices of positive linear electrical circuits with integer and fractional orders are investigated. It is shown that the stability, reachability and transfer matrix of positive linear systems are invariant under their integer and fractional orders.
5
Content available Positive electrical circuits with zero transfer matrices and their discretization
86%
Kaczorek T.
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tom Vol. 14
1--13
EN
Positive continuous–time and discrete–time linear electrical circuits with zero transfer matrices are addressed. It is shown that there exists a large class of positive electrical circuits with zero transfer matrices. The electrical circuits are unreachable, unobservable and unstable for all values of the resistances, inductances and capacitances. The discrete–time linear positive electrical circuits are introduced. It is shown that: 1) the discrete–time electrical circuit is asymptotically stable for all values of the discretization step if and only if the corresponding continuous–time electrical circuit is asymptotically stable; 2) the discretization of the continuous–time electrical circuit does not change their reachability, observability and transfer matrices.
6
Content available remote On the matrix techniques for modeling of thermoelastic waves in layered structures
86%
Verma K. L.
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tom Vol. 11, no 3
655-669
EN
The development of a general purpose model for thermoelastic wave propagation in Cartesian system for heat conducting isotropic layered plates is illustrated, the model can account for elastic and visco-elastic isotropic materials, single or multi-layered structures, and free or leaky systems. Theoretical treatment is presented for calculating the displacements, temperature, thermal stresses and temperature gradient within a multilayered plate in generalized theories of thermoelasticity, using the matrix transfer technique. Rigidly bonded and smooth interface condition is also considered as a special case to stimulate de-bonding of two materials layers. The model developed will be of value in material characterization and others quantitative information on thermo-mechanical, strength related properties of advanced materials. Relevant results of previous investigations and coupled thermoelasticity are deduced as special cases.
7
Content available Transfer matrices with positive coefficients of descriptor linear systems
86%
Kaczorek T. , Sajewski Ł.
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2024
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tom Vol. 6, No. 1
7--17
EN
Transfer matrices with positive coefficients of descriptor positive linear continuous-time systems are addressed. Two methods of checking of the positivity of descriptor linear systems are proposed. It is shown that if the positive descriptor system is asymptotically stable then all coefficients of its transfer matrix are positive.
8
Content available Invariant properties of positive linear electrical circuits
86%
Kaczorek T.
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nr 4
9
Content available Poles and zeros assignment by state feedbacks in positive linear systems
72%
Kaczorek T.
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tom Vol. 31, No. 3
593--605
EN
Poles and zeros assignment problem by state feedbacks in positive continuous-time and discrete-time systems is analyzed. It is shown that in multi-input multi-output positive linear systems by state feedbacks the poles and zeros of the transfer matrices can be assigned in the desired positions. In the positive continuous-time linear systems the feedback gain matrix can be chosen as a monomial matrix so that the poles and zeros of the transfer matrices have the desired values if the input matrix B is monomial. In the positive discrete-time linear systems to solve the problem the matrix B can be chosen monomial if and only if in every row and every column of the n × n system matrix A the sum of n−1 its entries is less than one.
10
Content available A new method for determination of positive realizations of linear continuous-time systems
72%
Kaczorek T.
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nr 5
11
Content available A new approach to the realization problem for fractional discrete-time linear systems
72%
Kaczorek T.
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tom Vol. 64, nr 1
9--14
EN
A new approach to the realization problem for fractional discrete-time linear systems is proposed. A procedure for computation of fractional realizations of given transfer matrices is presented and illustrated by numerical examples.
12
Content available Normalization of transfer matrix of linear systems by feedbacks
72%
Kaczorek T.
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tom Vol. 31, no 1
67-78
EN
The transfer matrix T(s) = C [Ins - A]^-1 B of a linear system x = Ax + Bu, y = Cx can be always written in the standard form T(s) = P(s)/d(s), where P(s) is the polynomial matrix and d(s) is the minimal common denominator. The irreducible transfer matrix is called normal if every nonzero second order minor of P(s) is divisible by d(s). It is shown that for an unnormal transfer matrix of the controllable system there exists a state-feedback gain matrix K such that the closed-loop system transfer matrix T(s) = C[Ins - (A + BK)]^-1 B is normal. In the case of the output-feedback the closed-loop transfer matrix Tc(s) = C (Ins - (A + BFC)]^-1 B can be made normal only if the system is controllable and observable.
13
Content available Computation of positive realizations for descriptor linear continuoustime systems
58%
Kaczorek T.
Autobusy : technika, eksploatacja, systemy transportowe
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2018
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tom R. 19, nr 12
428--432
EN
A new method for computation of positive realizations of given transfer matrices of descriptor linear continuous-time linear systems is proposed. Necessary and sufficient conditions for the existence of positive realizations of transfer matrices are given. A procedure for computation of the positive realizations is proposed and illustrated by examples.
PL
W pracy podano nową metodę wyznaczania dodatnich realizacji dla zadanych macierzy transmitacji operatorowych deskryptowych( singularnych) ciągłych układów liniowych. Sformułowano warunki konieczne i wystarczające istnienia dodatnich realizacji dla tej klasy deskryptowych ciągłych układów liniowych. Podano procedurę wyznaczania tych realizacji. Procedura ta została zlustrowana przykładami liczbowymi.
14
Content available Divisibility of the second-order minors of the nominators by minimal denominators of transfer matrices of cyclic fractional linear systems
58%
Kaczorek T.
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tom Vol. 31, no. 4
627--633
EN
The divisibility of the second-order minors of the numerators of transfer matrices by their minimal denominators for cyclic fractional linear systems is analyzed. It is shown that all nonzero second-order minors of the numerators of the transfer matrices are divisible by their minimal denominators if and only if the system matrices of fractional standard and descriptor linear systems are cyclic. The theorems are illustrated by examples of fractional standard and descriptor linear systems.
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