General response formula and minimum energy control of 2-D continuous-discrete linear systems

2002 ◽  
Author(s):  
T. Kaczorek
Keyword(s):  
Linear Systems ◽  
Minimum Energy ◽  
Energy Control ◽  
Discrete Linear Systems ◽  
Minimum Energy Control ◽  
General Response ◽  
Response Formula

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

2015 ◽  
Vol 25 (3) ◽  
pp. 319-331
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Control Problem ◽  
Linear Systems ◽  
Minimum Energy ◽  
Sufficient Conditions ◽  
Energy Control ◽  
Discrete Linear Systems ◽  
Minimum Energy Control ◽  
New Formulation ◽  
Necessary And Sufficient ◽  
The Given

AbstractA new formulation of the minimum energy control problem for the positive 2D continuous-discrete 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.

scholarly journals Minimum Energy Control of 2D Positive Continuous-Discrete Linear Systems

2014 ◽  
Vol 8 (3) ◽  
pp. 165-168
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Minimum Energy ◽  
Sufficient Conditions ◽  
Existence Of Solution ◽  
Energy Control ◽  
Final State ◽  
Discrete Linear Systems ◽  
Minimum Energy Control ◽  
One Step ◽  
Necessary And Sufficient

Abstract 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.

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.

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