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An extension of Klamka’s method to positive descriptor discrete-time linear systems with bounded inputs

Kaczorek T.

Archives of Control Sciences

2018

Vol. 28, No. 2

255--268

The minimum energy control problem for the positive descriptor discrete-time linear systems with bounded inputs by the use of Weierstrass-Kronecker decomposition is formulated and solved. Necessary and sufficient conditions for the positivity and reachability of descriptor discrete-time linear systems are given. Conditions for the existence of solution and procedure for computation of optimal input and the minimal value of the performance index is proposed and illustrated by a numerical example.

Minimum energy control of descriptor discrete-time linear systems by the use of Weierstrass-Kronecker decomposition

Kaczorek T., Borawski K.

Archives of Control Sciences

2016

Vol. 26, no. 2

177--187

The minimum energy control problem for the descriptor discrete-time linear systems by the use of Weierstrass-Kronecker decomposition is formulated and solved. Necessary and sufficient conditions for the reachability of descriptor discrete-time linear systems are given. A procedure for computation of optimal input and a minimal value of the performance index is proposed and illustrated by a numerical example.

Fractional descriptor standard and positive discrete-time nonlinear systems

Kaczorek T.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2015

Vol. 63, nr 3

651--655

A method of analysis of the fractional descriptor nonlinear discrete-time systems with regular pencils of linear part is proposed. The method is based on the Weierstrass-Kronecker decomposition of the pencils. Necessary and sufficient conditions for the positivity of the nonlinear systems are established. A procedure for computing the solution to the equations describing the nonlinear systems are proposed and demonstrated on a numerical example.

Descriptor standard and positive discrete-time nonlinear systems

Kaczorek T.

Archives of Control Sciences

2015

Vol. 25, no. 2

227--235

A method of analysis of descriptor nonlinear discrete-time systems with regular pencils of linear part is proposed. The method is based on the Weierstrass-Kronecker decomposition of the pencils. Necessary and sufficient conditions for the positivity of the nonlinear systems are established. A procedure for computing the solution to the equations describing the nonlinear systems are proposed and demonstrated on numerical examples.