scholarly journals Minimum Energy Control of Descriptor Fractional Discrete–Time Linear Systems with Two Different Fractional Orders

2017 ◽  
Vol 27 (1) ◽  
pp. 33-41 ◽  
Author(s):  
Łukasz Sajewski
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Minimum Energy ◽  
Decomposition Theorem ◽  
State Equation ◽  
Energy Control ◽  
Minimum Energy Control ◽  
Reachability Condition ◽  
Fractional Orders ◽  
Time Linear

Abstract 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.

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

2016 ◽  
Vol 26 (2) ◽  
pp. 177-187 ◽  
Author(s):  
Tadeusz Kaczorek ◽  
Kamil Borawski
Keyword(s):  
Control Problem ◽  
Linear Systems ◽  
Discrete Time ◽  
Performance Index ◽  
Minimum Energy ◽  
Sufficient Conditions ◽  
Energy Control ◽  
Minimum Energy Control ◽  
Necessary And Sufficient ◽  
Time Linear

Abstract 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.

Necessary and sufficient conditions for the minimum energy control of positive discrete-time linear systems with bounded inputs

2014 ◽  
Vol 62 (1) ◽  
pp. 85-89 ◽  
Author(s):  
T. Kaczorek
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Minimum Energy ◽  
Sufficient Conditions ◽  
Existence Of Solution ◽  
Necessary And Sufficient Conditions ◽  
Energy Control ◽  
Minimum Energy Control ◽  
Necessary And Sufficient ◽  
Time Linear

Abstract The minimum energy control problem for the positive discrete-time linear systems with bounded inputs is formulated and solved. Necessary and sufficient conditions for the existence of solution to the problem are established. A procedure for solving of the problem is proposed and illustrated by a numerical example.

scholarly journals Minimum energy control of fractional descriptor positive discrete-time linear systems

2014 ◽  
Vol 24 (4) ◽  
pp. 735-743 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Control Problem ◽  
Linear Systems ◽  
Discrete Time ◽  
Minimum Energy ◽  
Sufficient Conditions ◽  
Energy Control ◽  
Existence Of A Solution ◽  
Minimum Energy Control ◽  
Necessary And Sufficient ◽  
Time Linear

Abstract 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.

scholarly journals Controllability, reachability and minimum energy control of fractional discrete-time linear systems with multiple delays in state

2014 ◽  
Vol 62 (2) ◽  
pp. 233-239 ◽  
Author(s):  
M. Busłowicz
Keyword(s):  
Discrete Time ◽  
Minimum Energy ◽  
Sufficient Conditions ◽  
State Equation ◽  
Multiple Delays ◽  
Energy Control ◽  
Optimal Value ◽  
Minimum Energy Control ◽  
Necessary And Sufficient ◽  
Time Linear

Abstract In the paper the problems of controllability, reachability and minimum energy control of a fractional discrete-time linear system with delays in state are addressed. A general form of solution of the state equation of the system is given and necessary and sufficient conditions for controllability, reachability and minimum energy control are established. The problems are considered for systems with unbounded and bounded inputs. The considerations are illustrated by numerical examples. Influence of a value of the fractional order on an optimal value of the performance index of the minimum energy control is examined on an example.

scholarly journals Minimum energy control of positive discrete-time linear systems with bounded inputs

2013 ◽  
Vol 23 (2) ◽  
pp. 205-211 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Control Problem ◽  
Linear Systems ◽  
Discrete Time ◽  
Minimum Energy ◽  
Sufficient Conditions ◽  
Existence Of Solution ◽  
Energy Control ◽  
Numerical Example ◽  
Minimum Energy Control ◽  
Time Linear

The minimum energy control problem for the positive discrete-time linear systems with bounded inputs is formulated and solved. Sufficient conditions for the existence of solution to the problem are established. A procedure for solving of the problem is proposed and illustrated by a numerical example.

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