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 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 Analysis of Positive Linear Continuous–Time Systems Using the Conformable Derivative

2018 ◽  
Vol 28 (2) ◽  
pp. 335-340 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Asymptotic Stability ◽  
Linear System ◽  
Linear Systems ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Conformable Derivative ◽  
Continuous Time Systems ◽  
Necessary And Sufficient ◽  
Time Systems

Abstract Positive linear continuous-time systems are analyzed via conformable fractional calculus. A solution to a fractional linear system is derived. Necessary and sufficient conditions for the positivity of linear systems are established. Necessary and sufficient conditions for the asymptotic stability of positive linear systems are also given. The solutions of positive fractional linear systems based on the Caputo and conformable definitions are compared.

Positive fractional continuous-time linear systems with singular pencils

2012 ◽  
Vol 60 (1) ◽  
pp. 9-12 ◽  
Author(s):  
T. Kaczorek
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Descriptor Systems ◽  
State Variables ◽  
Algebraic Constraints ◽  
Necessary And Sufficient ◽  
Time Linear

Positive fractional continuous-time linear systems with singular pencils A method for checking the positivity and finding the solution to the positive fractional descriptor continuous-time linear systems with singular pencils is proposed. The method is based on elementary row and column operations of the fractional descriptor systems to equivalent standard systems with some algebraic constraints on state variables and inputs. Necessary and sufficient conditions for the positivity of the fractional descriptor systems are established.

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.

Decoupling zeros of positive continuous-time linear systems

2013 ◽  
Vol 61 (3) ◽  
pp. 557-562 ◽  
Author(s):  
T. Kaczorek
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Input Output ◽  
Necessary And Sufficient ◽  
Time Linear

Abstract Necessary and sufficient conditions for the reachability and observability of the positive continuous-time linear systems are established. Definitions of the input-decoupling zeros, output-decoupling zeros and input-output decoupling zeros are proposed. Some properties of the decoupling zeros are discussed.

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.

scholarly journals Fractional descriptor observers for fractional descriptor continuous-time linear system

2014 ◽  
Vol 24 (1) ◽  
pp. 27-37 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Design Procedure ◽  
Necessary And Sufficient Conditions ◽  
Numerical Examples ◽  
Necessary And Sufficient ◽  
Time Linear

Abstract Fractional descriptor full-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 demonstrated on two numerical examples.

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