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Content available Poles and zeros assignment by state feedbacks in positive linear systems
100%
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.
2
Content available Eigenvalues assignment in uncontrollable linear systems
100%
Kaczorek T.
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tom Vol. 70, nr 6
art. no. e141987
EN
It is shown that in uncontrollable linear system x = Ax + Bu it is possible to assign arbitrarily the eigenvalues of the closed-loop system with state feedbacks u = Kx, K ∈ ℜn⨉m if rank [A B] = n. The design procedure consists in two steps. In the step 1 a nonsingular matrix M ∈ ℜn⨉m is chosen so that the pair (MA,MB) is controllable. In step 2 the feedback matrix K is chosen so that the closed-loop matrix Ac = A − BK has the desired eigenvalues. The procedure is illustrated by simple example.
3
Content available Transformations of linear standard systems to positive asymptotically stable linear ones
100%
Kaczorek T.
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tom Vol. 34, no. 3
341--348
EN
New approaches to transformations of linear continuous-time systems to their positive asymptotically stable canonical controllable (observable) forms are proposed. It is shown that, if the system matrix is nonsingular, then the desired transformation matrix can be chosen in block diagonal form. Procedures for the computation of the transformation matrices are proposed and illustrated with simple numerical examples.
4
Content available Transformations of the matrices of linear systems to their canonical form with desired eigenvalues
100%
Kaczorek T.
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tom Vol. 71, nr 6
art. no. e147342
EN
A new approach to the transformations of the matrices of linear continuous-time systems to their canonical forms with desired eigenvalues is proposed. Conditions for the existence of solutions to the problems were given and illustrated by simple numerical examples.
5
Content available Exponential decay of transient values in discrete-time positive nonlinear systems
63%
Kaczorek T. , Ruszewski A.
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tom Vol. 32, No. 3
577--588
EN
The exponential decay of transient values in discrete-time nonlinear standard and fractional orders systems with linear positive linear part and positive feedbacks is investigated. Sufficient conditions for the exponential decay of transient values in this class of positive nonlinear systems are established. A procedure for computation of gains characterizing the class of nonlinear elements are given and illustrated on simple example.
6
Content available Positivity and cyclicity of descriptor electrical circuits with chain structure
63%
Kaczorek T. , Borawski K.
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tom Vol. 70, nr 1
art. no. e139955
EN
The positivity and cyclicity of descriptor linear electrical circuits with chain structure is considered. Two classes of descriptor linear electrical circuits are analyzed. Some new properties of these classes of electrical circuits are established. The results are extended to fractional descriptor linear electrical circuits.
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Content available Controllability and observability of the descriptor linear systems reduced to the standard ones by feedbacks
51%
Kaczorek T. , Klamka J. , Dzieliński A.
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2024
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tom Vol. 18, no. 1
119--122
EN
In this paper, a new method for the reduction of the descriptor linear systems to standards ones is presented and verified. The method uses a state and/or state derivative feedback of output and output derivative feedback in order to transform the descriptor system into a standard one. The controllability and observability properties of the original descriptor as well as transformed standard systems are proved. Simple numerical examples illustrate the theorems introduced.
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