Positive fractional 2D continuous-discrete linear systems

2011 ◽  
Vol 59 (4) ◽  
pp. 575-579 ◽  
Author(s):  
T. Kaczorek
Keyword(s):  
Linear Systems ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
New Class ◽  
Discrete Linear Systems ◽  
Necessary And Sufficient

Positive fractional 2D continuous-discrete linear systemsA new class of positive fractional 2D continuous-discrete linear systems is introduced. The solution to the equations describing by the new class of systems is derived. Necessary and sufficient conditions for the positivity of the fractional 2D continuous-discrete linear systems are established.

scholarly journals Stability of continuous-discrete linear systems with delays in state vector

2011 ◽  
Vol 21 (1) ◽  
pp. 25-36
Author(s):  
Tadeusz Kaczorek ◽  
Łukasz Sajewski
Keyword(s):  
Asymptotic Stability ◽  
Linear Systems ◽  
General Model ◽  
State Vector ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Numerical Example ◽  
New Class ◽  
Discrete Linear Systems ◽  
Necessary And Sufficient

Stability of continuous-discrete linear systems with delays in state vector A new class of positive continuous-discrete linear systems with delays in state vector described by the model based on 2D general model is addressed. Necessary and sufficient conditions for the positivity and asymptotic stability of this class of linear systems are established. A procedure for checking the asymptotic stability is proposed. The effectiveness of the procedure is demonstrated on a numerical example.

scholarly journals Reachability of Cone Fractional Continuous-Time Linear Systems

2009 ◽  
Vol 19 (1) ◽  
pp. 89-94 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Fractional Systems ◽  
New Class ◽  
Necessary And Sufficient ◽  
Time Linear

Reachability of Cone Fractional Continuous-Time Linear SystemsA new class of cone fractional continuous-time linear systems is introduced. Necessary and sufficient conditions for a fractional linear system to be a cone fractional one are established. Sufficient conditions for the reachability of cone fractional systems are given. The discussion is illustrated with an example of linear cone fractional systems.

Stability of continuous-discrete linear systems described by the general model

2011 ◽  
Vol 59 (2) ◽  
pp. 189-193 ◽  
Author(s):  
T. Kaczorek
Keyword(s):  
Asymptotic Stability ◽  
Linear Systems ◽  
General Model ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Discrete Linear Systems ◽  
Necessary And Sufficient ◽  
2D Model

Stability of continuous-discrete linear systems described by the general modelNew necessary and sufficient conditions for asymptotic stability of positive continuous-discrete linear systems described by the general 2D model are established. A procedure for checking the asymptotic stability is proposed. The effectiveness of the procedure is demonstrated on examples.

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 On a topology between Tα and Tγα

Filomat ◽  
2019 ◽  
Vol 33 (10) ◽  
pp. 3209-3221
Author(s):  
Dimitrije Andrijevic
Keyword(s):  
Topological Space ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Closure Operators ◽  
New Class ◽  
Necessary And Sufficient

Using the topology T in a topological space (X,T), a new class of generalized open sets called ?-preopen sets, is introduced and studied. This class generates a new topology Tg which is larger than T? and smaller than T??. By means of the corresponding interior and closure operators, among other results, necessary and sufficient conditions are given for Tg to coincide with T? , T? or T??.

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