scholarly journals Drazin inverse matrix method for fractional descriptor continuous-time linear systems

2014 ◽  
Vol 62 (3) ◽  
pp. 409-412 ◽  
Author(s):  
T. Kaczorek
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Matrix Method ◽  
Initial Conditions ◽  
Drazin Inverse ◽  
State Equations ◽  
Numerical Example ◽  
Continuous Time Systems ◽  
Time Systems ◽  
Time Linear

Abstract The Drazin inverse of matrices is applied to find the solutions of the state equations of the fractional descriptor continuous-time systems with regular pencils. An equality defining the set of admissible initial conditions for given inputs is derived. The proposed method is illustrated by a numerical example.

scholarly journals Application of the Drazin inverse to the analysis of descriptor fractional discrete-time linear systems with regular pencils

2013 ◽  
Vol 23 (1) ◽  
pp. 29-33 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Initial Conditions ◽  
The State ◽  
Drazin Inverse ◽  
State Equations ◽  
Numerical Example ◽  
Discrete Time Systems ◽  
Time Systems ◽  
Time Linear

The Drazin inverse of matrices is applied to find the solutions of the state equations of descriptor fractional discrete-time systems with regular pencils. An equality defining the set of admissible initial conditions for given inputs is derived. The proposed method is illustrated by a numerical example.

scholarly journals Drazin inverse matrix method for fractional descriptor discrete-time linear systems

2016 ◽  
Vol 64 (2) ◽  
pp. 395-399 ◽  
Author(s):  
T. Kaczorek
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Matrix Method ◽  
Initial Conditions ◽  
State Equation ◽  
The State ◽  
Drazin Inverse ◽  
State Equations ◽  
Numerical Example ◽  
Time Linear

Abstract The Drazin inverse of matrices is applied in order to find the solutions of the state equations of fractional descriptor discrete-time linear systems. The solution of the state equation is derived and the set of consistent initial conditions for a given set of admissible inputs is established. The proposed method is illustrated by a numerical example.

scholarly journals Fractional descriptor continuous–time linear systems described by the Caputo–Fabrizio derivative

2016 ◽  
Vol 26 (3) ◽  
pp. 533-541 ◽  
Author(s):  
Tadeusz Kaczorek ◽  
Kamil Borawski
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Numerical Example ◽  
Continuous Time Systems ◽  
Kronecker Theorem ◽  
Necessary And Sufficient ◽  
Time Systems ◽  
Time Linear

Abstract The Weierstrass–Kronecker theorem on the decomposition of the regular pencil is extended to fractional descriptor continuous-time linear systems described by the Caputo–Fabrizio derivative. A method for computing solutions of continuous-time systems is presented. Necessary and sufficient conditions for the positivity and stability of these systems are established. The discussion is illustrated with a numerical example.

scholarly journals SINGULAR FRACTIONAL CONTINUOUS-TIME AND DISCRETE-TIME LINEAR SYSTEMS

2013 ◽  
Vol 7 (1) ◽  
pp. 26-33 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Continuous Time ◽  
State Equation ◽  
Electrical Circuit ◽  
The State ◽  
Continuous Time Systems ◽  
Definition Of ◽  
Time Systems ◽  
Time Linear

Abstract New classes of singular fractional continuous-time and discrete-time linear systems are introduced. Electrical circuits are example of singular fractional continuous-time systems. Using the Caputo definition of the fractional derivative, the Weierstrass regular pencil decomposition and Laplace transformation the solution to the state equation of singular fractional linear systems is derived. It is shown that every electrical circuit is a singular fractional systems if it contains at least one mesh consisting of branches with only ideal supercondensators and voltage sources or at least one node with branches with supercoils. Using the Weierstrass regular pencil decomposition the solution to the state equation of singular fractional discrete-time linear systems is derived. The considerations are illustrated by numerical examples.

scholarly journals Computation of positive realizations for descriptor linear continuous-time systems

2018 ◽  
Vol 19 (12) ◽  
pp. 428-432
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
New Method ◽  
Transfer Matrices ◽  
Continuous Time Systems ◽  
Necessary And Sufficient ◽  
Time Systems ◽  
Time Linear

A new method for computation of positive realizations of given transfer matrices of descriptor linear continuous-time linear systems is proposed. Necessary and sufficient conditions for the existence of positive realizations of transfer matrices are given. A procedure for computation of the positive realizations is proposed and illustrated by examples.

scholarly journals Superstabilization of Descriptor Continuous-Time Linear Systems via State-Feedback Using Drazin Inverse Matrix Method

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 940
Author(s):  
Kamil Borawski
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Matrix Method ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Matrix Pencil ◽  
Inverse Matrix ◽  
Drazin Inverse ◽  
Feedback Gain ◽  
Time Linear

In this paper the descriptor continuous-time linear systems with the regular matrix pencil ( E , A ) are investigated using Drazin inverse matrix method. Necessary and sufficient conditions for the stability and superstability of this class of dynamical systems are established. The procedure for computation of the state-feedback gain matrix such that the closed-loop system is superstable is given. The effectiveness of the presented approach is demonstrated on numerical examples.

scholarly journals Reachability of standard and fractional continuous-time systems with constant inputs

2016 ◽  
Vol 26 (2) ◽  
pp. 147-159 ◽  
Author(s):  
Krzysztof Rogowski
Keyword(s):  
Continuous Time ◽  
Initial Conditions ◽  
Sufficient Conditions ◽  
Final State ◽  
Continuous Time Systems ◽  
Necessary And Sufficient ◽  
Time Systems ◽  
The Given ◽  
Time Linear ◽  
Order Continuous

Abstract The reachability of standard and fractional-order continuous-time systems with constant inputs is addressed. Positive and non-positive continuous-time linear systems are considered. Necessary and sufficient conditions for the existence of such constant inputs that steers the system from zero initial conditions to the given final state in desired time are derived and proved. As an example of such systems the electrical circuits with DC voltage sources are presented.

scholarly journals Minimum energy control of fractional positive continuous-time linear systems using Caputo-Fabrizio definition

2017 ◽  
Vol 65 (1) ◽  
pp. 45-51 ◽  
Author(s):  
T. Kaczorek
Keyword(s):  
Fractional Derivative ◽  
Linear Systems ◽  
Continuous Time ◽  
Minimum Energy ◽  
Energy Control ◽  
Continuous Time Systems ◽  
Minimum Energy Control ◽  
Definition Of ◽  
Time Systems ◽  
Time Linear

Abstract The Caputo-Fabrizio definition of the fractional derivative is applied to minimum energy control of fractional positive continuous- time linear systems with bounded inputs. Conditions for the reachability of standard and positive fractional linear continuous-time systems are established. The minimum energy control problem for the fractional positive linear systems with bounded inputs is formulated and solved.

scholarly journals Design of regular positive and stable descriptor systems via state-feedbacks for descriptor continuous-time linear systems with singular pencils

2014 ◽  
Vol 24 (3) ◽  
pp. 289-297
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Special Form ◽  
The State ◽  
New Method ◽  
Descriptor Systems ◽  
Descriptor System ◽  
Asymptotically Stable ◽  
Numerical Example ◽  
Time Linear

Abstract A new method is proposed of design of regular positive and asymptotically stable descriptor systems by the use of state-feedbacks for descriptor continuous-time linear systems with singular pencils. The method is based on the reduction of the descriptor system by elementary row and column operations to special form. A procedure for the design of the state-feedbacks gain matrix is presented and illustrated by a numerical example

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