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Minimum energy control of descriptor fractional discrete-time linear systems with two different fractional orders

100%
Sajewski Ł.
International Journal of Applied Mathematics and Computer Science
|
2017
|
tom 27
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nr 1
33-41
EN
Reachability and minimum energy control of descriptor fractional discrete-time linear systems with different fractional orders are addressed. Using the Weierstrass-Kronecker decomposition theorem of the regular pencil, a solution to the state equation of descriptor fractional discrete-time linear systems with different fractional orders is given. The reachability condition of this class of systems is presented and used for solving the minimum energy control problem. The discussion is illustrated with numerical examples.
2
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Minimum energy control of positive continuous-time linear systems with bounded inputs

100%
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2013
|
tom 23
|
nr 4
725-730
EN
The minimum energy control problem for positive continuous-time linear systems with bounded inputs is formulated and solved. Sufficient conditions for the existence of a solution to the problem are established. A procedure for solving the problem is proposed and illustrated with a numerical example.
3
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Minimum energy control of fractional positive continuous-time linear systems with bounded inputs

100%
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2014
|
tom 24
|
nr 2
335-340
EN
A minimum energy control problem for fractional positive continuous-time linear systems with bounded inputs is formulated and solved. Sufficient conditions for the existence of a solution to the problem are established. A procedure for solving the problem is proposed and illustrated with a numerical example.
4
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Minimum energy control of fractional descriptor positive discrete-time linear systems

100%
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2014
|
tom 24
|
nr 4
735-743
EN
Necessary and sufficient conditions for the positivity and reachability of fractional descriptor positive discrete-time linear systems are established. The minimum energy control problem for descriptor positive systems is formulated and solved. Sufficient conditions for the existence of a solution to the minimum energy control problem are given. A procedure for computation of optimal input sequences and a minimal value of the performance index is proposed and illustrated by a numerical example.
5
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Stochastic controllability of linear systems with state delays

88%
Klamka J.
International Journal of Applied Mathematics and Computer Science
|
2007
|
tom 17
|
nr 1
5-13
EN
A class of finite-dimensional stationary dynamic control systems described by linear stochastic ordinary differential state equations with a single point delay in the state variables is considered. Using a theorem and methods adopted directly from deterministic controllability problems, necessary and sufficient conditions for various kinds of stochastic relative controllability are formulated and proved. It will be demonstrated that under suitable assumptions the relative controllability of an associated deterministic linear dynamic system is equivalent to the stochastic relative exact controllability and the stochastic relative approximate controllability of the original linear stochastic dynamic system. Some remarks and comments on the existing results for the controllability of linear dynamic systems with delays are also presented. Finally, a minimum energy control problem for a stochastic dynamic system is formulated and solved.
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