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Zeroing of state variables in fractional descriptor electrical circuits by state-feedbacks

Kaczorek T.

Archives of Electrical Engineering

2014

Vol. 63, nr 3

321--333

The problem of zeroing of the state variables in fractional descriptor electrical circuits by state-feedbacks is formulated and solved. Necessary and sufficient conditions for the existence of gain matrices such that the state variables of closed-loop systems are zero for time greater zero are established. The procedure of choice of the gain matrices is demonstrated on simple descriptor electrical circuits with regular pencils.

Pointwise completeness and pointwise degeneracy of 2D standard and positive Fornasini-Marchesini models with state-feedbacks

Kaczorek T.

Control and Cybernetics

2011

Vol. 40, no 1

39-58

Necessary and sufficient conditions are established for the pointwise completeness of 2D standard and positive Fornasini-Marchesini models with state-feedbacks. Similar relations are obtained for the pointwise degeneracy of the 2D models with state-feedbacks. It is shown that if the positive 2D model is pointwise complete then there exists a gain matrix of the state-feedback such that the closed-loop system is pointwise degenerated if both matrices B1 and B2 of the 2D Fornasini-Marchesini model are nonzero. The considerations are illustrated by numerical examples.

Pointwise completeness and pointwise degeneracy of standard and positive linear systems with state-feedbacks

Kaczorek T.

Journal of Automation Mobile Robotics and Intelligent Systems

2010

Vol. 4, No. 1

3-7

The pointwise completeness and pointwise degeneracy of standard and positive linear discrete-time and continuous- time systems with state-feedbacks are addressed. It is shown that: 1) the pointwise completeness and pointwise degeneracy of continuous-time standard systems are invariant under the state and output feedbacks, 2) for standard and positive discrete-time and positive continuous- time systems necessary and sufficient conditions are established for the existence of gain matrices of statefeedbacks such that the closed-loop systems are pointwise complete. Considerations are illustrated by numerical examples.

Positivity and stabilization of fractional 2D Roesser model by state-feedbacks, LMI approach

Kaczorek T.

Archives of Control Sciences

2009

Vol. 19, no. 2

165-177

LMI approach is applied to compute a gain matrix of state-feedbacks such that the closed-loop system is positive and asymptotically stable. Necessary and suffiecient conditions for the solvability of the problem are established. The proposed method is illustrated by two numerical examples.