Realization Problem of 1D Standard Linear Systems

2014 ◽  
pp. 1-66
Author(s):  
Tadeusz Kaczorek ◽  
Łukasz Sajewski
Keyword(s):  
Linear Systems ◽  
Realization Problem ◽  
Standard Linear

scholarly journals Computation of positive realization of MIMO hybrid linear systems in the form of second Fornasini-Marchesini model

2010 ◽  
Vol 20 (3) ◽  
pp. 267-285 ◽  
Author(s):  
Tadeusz Kaczorek ◽  
Łukasz Sajewski
Keyword(s):  
Linear Systems ◽  
Hybrid Systems ◽  
Transfer Matrix ◽  
Sufficient Conditions ◽  
The State ◽  
Realization Problem ◽  
Numerical Example ◽  
State Variable

Computation of positive realization of MIMO hybrid linear systems in the form of second Fornasini-Marchesini modelThe realization problem for positive multi-input and multi-output (MIMO) linear hybrid systems with the form of second Fornasini-Marchesini model is formulated and a method based on the state variable diagram for finding a positive realization of a given proper transfer matrix is proposed. Sufficient conditions for the existence of the positive realization of a given proper transfer matrix are established. A procedure for computation of a positive realization is proposed and illustrated by a numerical example.

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.

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.

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