scholarly journals Descriptor fractional linear systems with regular pencils

2013 ◽  
Vol 23 (2) ◽  
pp. 309-315 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Laplace Transform ◽  
Linear Systems ◽  
Discrete Time ◽  
Continuous Time ◽  
The State ◽  
Transition Matrices ◽  
State Equations ◽  
Numerical Examples ◽  
The Laplace Transform ◽  
Time Linear

Methods for finding solutions of the state equations of descriptor fractional discrete-time and continuous-time linear systems with regular pencils are proposed. The derivation of the solution formulas is based on the application of the Z transform, the Laplace transform and the convolution theorems. Procedures for computation of the transition matrices are proposed. The efficiency of the proposed methods is demonstrated on simple numerical examples.

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.

Comparison of Different Models of Positive Fractional Continuous-Time Linear Systems and Electrical Circuits Based on the Step Responses

2017 ◽  
Vol 260 ◽  
pp. 147-155
Author(s):  
Kamil Borawski
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
State Equations ◽  
Electrical Circuits ◽  
Fractional Systems ◽  
Numerical Examples ◽  
Necessary And Sufficient ◽  
Time Linear ◽  
Step Responses

The step responses of positive fractional continuous-time linear systems and electrical circuits described by different models will be investigated and comparison of the models will be performed. Solutions to the state equations of continuous-time linear systems described by Caputo and Caputo-Fabrizio derivatives and necessary and sufficient conditions of the positivity of fractional systems will be recalled. Considerations will be illustrated by numerical examples.

scholarly journals Comparison of approximation methods of positive stable continuous-time linear systems by positive stable discrete-time systems

2013 ◽  
Vol 62 (2) ◽  
pp. 345-355 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Continuous Time ◽  
Electrical Circuit ◽  
Approximation Methods ◽  
Asymptotically Stable ◽  
Numerical Examples ◽  
Discrete Time Systems ◽  
Time Systems ◽  
Time Linear

Abstract The positive asymptotically stable continuous-time linear systems are approximated by corresponding asymptotically stable discrete-time linear systems. Two methods of the approximation are presented and the comparison of the methods is addressed. The considerations are illustrated by three numerical examples and an example of positive electrical circuit.

scholarly journals Fractional Positive Continuous-Time Linear Systems and Their Reachability

2008 ◽  
Vol 18 (2) ◽  
pp. 223-228 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Positive Systems ◽  
State Equations ◽  
Fractional Systems ◽  
New Class ◽  
The Laplace Transform ◽  
Necessary And Sufficient ◽  
Time Linear

Fractional Positive Continuous-Time Linear Systems and Their ReachabilityA new class of fractional linear continuous-time linear systems described by state equations is introduced. The solution to the state equations is derived using the Laplace transform. Necessary and sufficient conditions are established for the internal and external positivity of fractional systems. Sufficient conditions are given for the reachability of fractional positive systems.

scholarly journals On controllability and observability of fractional continuous-time linear systems with regular pencils

2017 ◽  
Vol 65 (3) ◽  
pp. 297-304
Author(s):  
A. Younus ◽  
I. Javaid ◽  
A. Zehra
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
The State ◽  
Necessary And Sufficient Conditions ◽  
State Equations ◽  
Necessary And Sufficient ◽  
Controllability And Observability ◽  
Time Linear

AbstractIn this paper necessary and sufficient conditions of controllability and observability for solutions of the state equations of fractional continuous time linear systems with regular pencils are proposed. The derivations of the conditions are based on the construction of Gramian matrices.

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 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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