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.

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.

Asymptotic stability of positive 2D linear systems with delays

2009 ◽  
Vol 57 (2) ◽  
pp. 133-138 ◽  
Author(s):  
T. Kaczorek
Keyword(s):  
Asymptotic Stability ◽  
Linear Systems ◽  
General Model ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Roesser Model ◽  
Numerical Examples ◽  
Necessary And Sufficient

Asymptotic stability of positive 2D linear systems with delays New necessary and sufficient conditions for the asymptotic stability of positive 2D linear systems with delays described by the general model, Fornasini-Marchesini models and Roesser model are established. It is shown that checking of the asymptotic stability of positive 2D linear systems with delays can be reduced to the checking of the asymptotic stability of corresponding positive 1D linear systems without delays. The efficiency of the new criterions is demonstrated on numerical examples.

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 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.

Necessary and sufficient conditions for stability of fractional discrete-time linear state-space systems

2013 ◽  
Vol 61 (4) ◽  
pp. 779-786 ◽  
Author(s):  
M. Busłowicz ◽  
A. Ruszewski
Keyword(s):  
Asymptotic Stability ◽  
Linear Systems ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
The State ◽  
Necessary And Sufficient Conditions ◽  
Practical Stability ◽  
State Matrix ◽  
Necessary And Sufficient ◽  
Time Linear

Abstract In the paper the problems of practical stability and asymptotic stability of fractional discrete-time linear systems are addressed. Necessary and sufficient conditions for practical stability and for asymptotic stability are established. The conditions are given in terms of eigenvalues of the state matrix of the system. In particular, it is shown that (similarly as in the case of fractional continuous-time linear systems) in the complex plane exists such a region, that location of all eigenvalues of the state matrix in this region is necessary and sufficient for asymptotic stability. The parametric description of boundary of this region is given. Moreover, it is shown that Schur stability of the state matrix (all eigenvalues have absolute values less than 1) is not necessary nor sufficient for asymptotic stability of the fractional discrete-time system. The considerations are illustrated by numerical examples.

scholarly journals New stability conditions for positive continuous-discrete 2D linear systems

2011 ◽  
Vol 21 (3) ◽  
pp. 521-524 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Asymptotic Stability ◽  
Linear Systems ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Stability Conditions ◽  
Stability Tests ◽  
Numerical Examples ◽  
The Stability ◽  
Necessary And Sufficient

New stability conditions for positive continuous-discrete 2D linear systemsNew necessary and sufficient conditions for asymptotic stability of positive continuous-discrete 2D linear systems are established. Necessary conditions for the stability are also given. The stability tests are demonstrated on numerical examples.

scholarly journals Reachability of linear hybrid systems described by the general model

2010 ◽  
Vol 20 (2) ◽  
pp. 199-207 ◽  
Author(s):  
Tadeusz Kaczorek ◽  
Krzysztof Rogowski
Keyword(s):  
Linear Systems ◽  
Hybrid Systems ◽  
Hybrid System ◽  
General Model ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sufficient Condition ◽  
Numerical Examples ◽  
Necessary And Sufficient

Reachability of linear hybrid systems described by the general modelThe reachability of standard and positive hybrid linear systems described by the general model is addressed. Necessary and sufficient conditions for the reachability of the standard general model are established. Sufficient condition is given for the reachability of positive hybrid system described by the general model. The considerations are illustrated by numerical examples.

scholarly journals Asymptotic stability of positive fractional 2D linear systems

2009 ◽  
Vol 57 (3) ◽  
pp. 289-292 ◽  
Author(s):  
T. Kaczorek
Keyword(s):  
Asymptotic Stability ◽  
Linear Systems ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
2D Systems ◽  
The Stability ◽  
Necessary And Sufficient

Asymptotic stability of positive fractional 2D linear systemsNew necessary and sufficient conditions for the asymptotic stability of the positive fractional 2D systems are established. It is shown that the checking of the asymptotic stability of positive fractional 2D linear systems can be reduced to testing the stability of corresponding 1D positive linear systems.

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.

Asymptotic stability of heteroclinic cycles in systems with symmetry. II

2004 ◽  
Vol 134 (6) ◽  
pp. 1177-1197 ◽  
Author(s):  
Martin Krupa ◽  
Ian Melbourne
Keyword(s):  
Asymptotic Stability ◽  
Transition Matrix ◽  
Sufficient Conditions ◽  
Systematic Investigation ◽  
Necessary And Sufficient Conditions ◽  
Sufficient Condition ◽  
Heteroclinic Cycles ◽  
Higher Dimensional ◽  
Necessary And Sufficient

Systems possessing symmetries often admit robust heteroclinic cycles that persist under perturbations that respect the symmetry. In previous work, we began a systematic investigation into the asymptotic stability of such cycles. In particular, we found a sufficient condition for asymptotic stability, and we gave algebraic criteria for deciding when this condition is also necessary. These criteria are satisfied for cycles in R3.Field and Swift, and Hofbauer, considered examples in R4 for which our sufficient condition for stability is not optimal. They obtained necessary and sufficient conditions for asymptotic stability using a transition-matrix technique.In this paper, we combine our previous methods with the transition-matrix technique and obtain necessary and sufficient conditions for asymptotic stability for a larger class of heteroclinic cycles. In particular, we obtain a complete theory for ‘simple’ heteroclinic cycles in R4 (thereby proving and extending results for homoclinic cycles that were stated without proof by Chossat, Krupa, Melbourne and Scheel). A partial classification of simple heteroclinic cycles in R4 is also given. Finally, our stability results generalize naturally to higher dimensions and many of the higher-dimensional examples in the literature are covered by this theory.

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