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Minimum energy control of positive 2D continuous-discrete linear systems with bounded inputs

Kaczorek T.

Archives of Control Sciences

2015

Vol. 25, no. 3

319--331

A new formulation of the minimum energy control problem for the positive 2D continuousdiscrete linear systems with bounded inputs is proposed. Necessary and sufficient conditions for the reachability of the systems are established. Conditions for the existence of the solution to the minimum energy control problem and a procedure for computation of an input minimizing the given performance index are given. Effectiveness of the procedure is demonstrated on numerical example.

Minimum energy control of 2D positive continuous-discrete linear systems

Kaczorek T.

Acta Mechanica et Automatica

2014

Vol. 8, no. 3

165--168

The minimum energy control problem for the 2D positive continuous-discrete linear systems is formulated and solved. Necessary and sufficient conditions for the reachability at the point of the systems are given. Sufficient conditions for the existence of solution to the problem are established. It is shown that if the system is reachable then there exists an optimal input that steers the state from zero boundary conditions to given final state and minimizing the performance index for only one step (q = 1). A procedure for solving of the problem is proposed and illustrated by a numerical example.

Reduction of descriptor 2D continuous-discrete linear systems to standard systems

Kaczorek T.

Pomiary Automatyka Kontrola

2012

R. 58, nr 9

809-814

A method of reduction of descriptor 2D continuous-discrete linear systems with regular pencil to equivalent standard linear systems is proposed. The method is based on the shuffle algorithm. A polynomial matrix version of the method is also given. The inverse problem of reduction of standard systems to descriptor systems is considered as well.

W pracy podano metodę redukcji singularnych układów 2W ciągło-dyskretnych o pękach regularnych do równoważnych układów standardowych. Metoda ta opiera się na algorytmie przesuwania. Podano również wersję wielomianową tej metody opartą na działaniach elementarnych na macierzach wielomianowych. Pokazano, że odwracając procedurę metody wielomianowej można przekształcić układ standardowy do układu singularnego.

Positive realizations with reduced numbers of delays for 2D continuous-discrete linear systems

Kaczorek T.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2012

Vol. 60, nr 4

835-840

A new method is proposed for determination of positive realizations with reduced numbers of delays of linear 2D continuousdiscrete systems. Sufficient conditions for the existence of the positive realizations of a given proper transfer function are established. It is shown that there exists a positive realization with reduced numbers of delays if there exists a positive realization without delays but with a greater dimension. The proposed method is demonstrated on a numerical example.