Positivity of descriptor linear systems with regular pencils

2012 ◽  
Vol 61 (1) ◽  
pp. 101-113 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Positive Systems ◽  
Electrical Circuits ◽  
Numerical Examples ◽  
Standard Linear ◽  
Descriptor Linear Systems ◽  
The Relationship ◽  
Equivalent Conditions ◽  
Time Linear

Positivity of descriptor linear systems with regular pencilsThe positivity of descriptor continuous-time and discrete-time linear systems with regular pencils are addressed. Such systems can be reduced to standard linear systems and can be decomposed into dynamical and static parts. Two definitions of the positive systems are proposed. It is shown that the definitions are not equivalent. Conditions for the positivity of the systems and the relationship between two classes of positive systems are established. The considerations are illustrated by examples of electrical circuits and 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 Perfect observer resistant to the changes of dynamics of the standard linear system

2017 ◽  
Vol 65 (3) ◽  
pp. 313-316
Author(s):  
M. A. Sławiński
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Continuous Time ◽  
Numerical Examples ◽  
Standard Linear ◽  
Time Linear

AbstractThe article presents a class of perfect observers for standard continuous-time linear systems. Observers are resistant to significant changes in the dynamics of the system. The value of poles of the system can be unlimited as long as their number does not change and the conditions presented in this article are satisfied. There are presented numerical examples and simulations results.

scholarly journals Checking of the positivity of descriptor linear systems by the use of the shuffle algorithm

2011 ◽  
Vol 21 (3) ◽  
pp. 287-298 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Equivalent Form ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Descriptor Systems ◽  
State Equations ◽  
Necessary And Sufficient ◽  
Descriptor Linear Systems ◽  
Time Linear

Checking of the positivity of descriptor linear systems by the use of the shuffle algorithmNecessary and sufficient conditions for the positivity of descriptor continuous-time and discrete-time linear systems are established. The shuffle algorithm is applied to transform the state equations of the descriptor systems to their equivalent form for which necessary and sufficient conditions for their positivity have been derived. A procedure for checking the positivity of the descriptor systems is proposed and illustrated by numerical examples.

scholarly journals Positive time-varying continuous-time linear systems and electrical circuits

2015 ◽  
Vol 63 (4) ◽  
pp. 837-842 ◽  
Author(s):  
T. Kaczorek
Keyword(s):  
Large Class ◽  
Linear Systems ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Electrical Circuits ◽  
Time Varying Parameters ◽  
Positive Time ◽  
Necessary And Sufficient ◽  
Time Linear

AbstractThe positivity of time-varying continuous-time linear systems and electrical circuits are addressed. Necessary and sufficient conditions for the positivity of the systems and electrical circuits are established. It is shown that there exists a large class of positive electrical circuits with time-varying parameters. Examples of positive electrical circuits are presented.

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.

scholarly journals Reduced-order fractional descriptor observers for fractional descriptor continuous-time linear system

2014 ◽  
Vol 62 (4) ◽  
pp. 889-895 ◽  
Author(s):  
T. Kaczorek
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Design Procedure ◽  
Necessary And Sufficient Conditions ◽  
Reduced Order ◽  
Numerical Examples ◽  
Necessary And Sufficient ◽  
Time Linear

Abstract Fractional descriptor reduced-order observers for fractional descriptor continuous-time linear systems are proposed. Necessary and sufficient conditions for the existence of the observers are established. The design procedure of the observers is given and is demonstrated on two numerical examples.

scholarly journals Decentralized stabilization of fractional positive descriptor continuous-time linear systems

2018 ◽  
Vol 28 (1) ◽  
pp. 135-140 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Decentralized Stabilization ◽  
Numerical Example ◽  
Necessary And Sufficient ◽  
Descriptor Linear Systems ◽  
Time Linear

AbstractA method for decentralized stabilization of fractional positive descriptor linear systems is proposed. Necessary and sufficient conditions for decentralized stabilization of fractional positive descriptor linear systems are established. The efficiency of the proposed method is demonstrated on a numerical example.

scholarly journals Robust stability of positive continuous-time linear systems with delays

2010 ◽  
Vol 20 (4) ◽  
pp. 665-670 ◽  
Author(s):  
Mikołaj Busłowicz
Keyword(s):  
Linear Systems ◽  
Robust Stability ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Numerical Examples ◽  
Structured Perturbations ◽  
Uncertainty Structure ◽  
Necessary And Sufficient ◽  
Time Linear

Robust stability of positive continuous-time linear systems with delaysThe paper is devoted to the problem of robust stability of positive continuous-time linear systems with delays with structured perturbations of state matrices. Simple necessary and sufficient conditions for robust stability in the general case and in the case of systems with a linear uncertainty structure in two sub-cases: (i) a unity rank uncertainty structure and (ii) nonnegative perturbation matrices are established. The problems are illustrated with numerical examples.

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