scholarly journals A new approach to the realization problem for fractional discrete-time linear systems

2016 ◽  
Vol 64 (1) ◽  
pp. 9-14 ◽  
Author(s):  
T. Kaczorek
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Transfer Matrices ◽  
Realization Problem ◽  
New Approach ◽  
Numerical Examples ◽  
Time Linear

Abstract A new approach to the realization problem for fractional discrete-time linear systems is proposed. A procedure for computation of fractional realizations of given transfer matrices is presented and illustrated by numerical examples.

Positive and asymptotically stable realizations for descriptor discrete-time linear systems

2013 ◽  
Vol 61 (1) ◽  
pp. 229-237
Author(s):  
T. Kaczorek
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Asymptotically Stable ◽  
Transfer Matrices ◽  
Numerical Examples ◽  
Time Linear

Abstract Conditions for the existence of positive and asymptotically stable realizations for descriptor discrete-time linear systems are established. Procedures for computation of positive and asymptotically stable realizations for improper transfer matrices are proposed. The effectiveness of the methods is demonstrated on numerical examples

scholarly journals A new approach to constrained state estimation for discrete-time linear systems with unknown inputs

2017 ◽  
Vol 28 (1) ◽  
pp. 326-341 ◽  
Author(s):  
Jose Fernando Garcia Tirado ◽  
Alejandro Marquez-Ruiz ◽  
Hector Botero Castro ◽  
Fabiola Angulo
Keyword(s):  
State Estimation ◽  
Linear Systems ◽  
Discrete Time ◽  
New Approach ◽  
Unknown Inputs ◽  
Time Linear

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 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.

An Output Feedback Approach to Enlarging the Controllable Region for Systems Subject to Actuator Saturation

2011 ◽  
Vol 71-78 ◽  
pp. 4256-4260
Author(s):  
Hong Bo Zou ◽  
Hui Hui Feng ◽  
Xiao Dong Zhao
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Output Feedback ◽  
Actuator Saturation ◽  
Precise Description ◽  
New Approach ◽  
Input Amplitude ◽  
Simulation Results ◽  
Implementation Method ◽  
Time Linear

The problem of output feedback for the unstable discrete-time linear systems with input amplitude constraints is studied. Based on the precise description of controllable region, the typical implementation method of observer-based output feedback will decrease the system’s controllable region, a new approach is proposed in this paper, which make the system’s controllable domain as big as possible. Finally, two illustrative examples and simulation results are given to demonstrate the effectiveness of the proposed method.

Relationship between controllability and observability of standard and fractional different orders discrete-time linear system

2019 ◽  
Vol 22 (1) ◽  
pp. 158-169 ◽  
Author(s):  
Tadeusz Kaczorek ◽  
Łukasz Sajewski
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Fractional Order ◽  
Discrete Time ◽  
Numerical Examples ◽  
Controllability And Observability ◽  
The Relationship ◽  
Time Linear

Abstract The controllability and observability of fractional different orders discrete-time linear systems are analyzed. The relationship between controllability and observability of standard and fractional discrete-time linear systems are investigated. The influence of the fractional order on the controllability and observability is shown. Investigations are illustrated on numerical examples.

scholarly journals Simple Conditions for Practical Stability of Positive Fractional Discrete-Time Linear Systems

2009 ◽  
Vol 19 (2) ◽  
pp. 263-269 ◽  
Author(s):  
Mikołaj Busłowicz ◽  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Practical Stability ◽  
Practical Implementation ◽  
Numerical Examples ◽  
Discrete Time Systems ◽  
Necessary And Sufficient ◽  
Time Systems ◽  
Time Linear

Simple Conditions for Practical Stability of Positive Fractional Discrete-Time Linear SystemsIn the paper the problem of practical stability of linear positive discrete-time systems of fractional order is addressed. New simple necessary and sufficient conditions for practical stability and for practical stability independent of the length of practical implementation are established. It is shown that practical stability of the system is equivalent to asymptotic stability of the corresponding standard positive discrete-time systems of the same order. The discussion is illustrated with numerical examples.

scholarly journals A new method for computation of positive realizations of linear discrete-time systems

2021 ◽  
pp. 3-8
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
New Method ◽  
Transfer Matrices ◽  
Discrete Time Systems ◽  
Time Systems ◽  
Time Linear

A new method for computation of positive realizations of given transfer matrices of linear discrete-time linear systems is proposed. 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 an example.  

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