scholarly journals Positivity and Asymptotic Stability of Descriptor Linear Systems with Regular Pencils

2014 ◽  
Vol 24 (2) ◽  
pp. 193-205 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Asymptotic Stability ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Drazin Inverse ◽  
Matrix Approach ◽  
Numerical Examples ◽  
Discrete Time Systems ◽  
Necessary And Sufficient ◽  
Time Systems ◽  
Descriptor Linear Systems

Abstract The positivity and asymptotic stability of the descriptor linear continuous-time and discrete-time systems with regular pencils are addressed. Necessary and sufficient conditions for the positivity and asymptotic stability of the systems are established using the Drazin inverse matrix approach. Effectiveness of the conditions are demonstrated on numerical examples.

Positive stable realizations of discrete-time linear systems

2012 ◽  
Vol 60 (3) ◽  
pp. 605-616
Author(s):  
T. Kaczorek
Keyword(s):  
Transfer Function ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Asymptotically Stable ◽  
Numerical Examples ◽  
Discrete Time Systems ◽  
Necessary And Sufficient ◽  
Time Systems ◽  
Time Linear

Abstract The problem of existence and determination of the set of positive asymptotically stable realizations of a proper transfer function of linear discrete-time systems is formulated and solved. Necessary and sufficient conditions for existence of the set of the realizations are established. A procedure for computation of the set of realizations are proposed and illustrated by numerical examples.

scholarly journals Absolute stability of a class of fractional positive nonlinear systems

2019 ◽  
Vol 29 (1) ◽  
pp. 93-98 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Continuous Time ◽  
Absolute Stability ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Discrete Time Systems ◽  
The Absolute ◽  
Necessary And Sufficient ◽  
Time Systems

Abstract The positivity and absolute stability of a class of fractional nonlinear continuous-time and discrete-time systems are addressed. Necessary and sufficient conditions for the positivity of this class of nonlinear systems are established. Sufficient conditions for the absolute stability of this class of fractional positive nonlinear systems are also given.

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.

scholarly journals Simple Conditions for Practical Stability of Positive Fractional Discrete-Time Linear Systems

2009 ◽  
Vol 19 (2) ◽  
pp. 263-269 ◽  
Author(s):  
Mikołaj Busłowicz ◽  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Practical Stability ◽  
Practical Implementation ◽  
Numerical Examples ◽  
Discrete Time Systems ◽  
Necessary And Sufficient ◽  
Time Systems ◽  
Time Linear

Simple Conditions for Practical Stability of Positive Fractional Discrete-Time Linear SystemsIn the paper the problem of practical stability of linear positive discrete-time systems of fractional order is addressed. New simple necessary and sufficient conditions for practical stability and for practical stability independent of the length of practical implementation are established. It is shown that practical stability of the system is equivalent to asymptotic stability of the corresponding standard positive discrete-time systems of the same order. The discussion is illustrated with numerical examples.

scholarly journals On Controllability of Fractional Continuous-Time Systems

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Mina Ghasemi ◽  
Kameleh Nassiri
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Fractional Systems ◽  
Numerical Examples ◽  
Continuous Time Systems ◽  
Fractional System ◽  
Necessary And Sufficient ◽  
Time Systems

The aim of this paper is to study the controllability of fractional systems involving the Atangana–Baleanu fractional derivative using the Caputo approach. In the first step, the solution of a linear fractional system is obtained. Then, based on the obtained solution, some necessary and sufficient conditions for the controllability of such a system will be presented. Afterwards, the controllability of a nonlinear fractional system will be analyzed, based on these results. Our tool for the presentation of the sufficient conditions of controllability in this part is Schauder fixed point theorem. In the last step, the analytical results are illustrated by numerical examples.

scholarly journals Descriptor standard and positive discrete-time nonlinear systems

2015 ◽  
Vol 25 (2) ◽  
pp. 227-235 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Linear Part ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Numerical Examples ◽  
Discrete Time Systems ◽  
Necessary And Sufficient ◽  
Time Systems

AbstractA method of analysis of descriptor nonlinear discrete-time systems with regular pencils of linear part is proposed. The method is based on the Weierstrass-Kronecker decomposition of the pencils. Necessary and sufficient conditions for the positivity of the nonlinear systems are established. A procedure for computing the solution to the equations describing the nonlinear systems are proposed and demonstrated on numerical examples.

scholarly journals Positivity of Fractional Descriptor Linear Discrete–Time Systems

2019 ◽  
Vol 29 (2) ◽  
pp. 305-310
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Discrete Time ◽  
Sufficient Conditions ◽  
State Equation ◽  
The State ◽  
Necessary And Sufficient Conditions ◽  
Numerical Examples ◽  
Discrete Time Systems ◽  
Necessary And Sufficient ◽  
Time Systems

Abstract The positivity of fractional descriptor linear discrete-time systems is investigated. The solution to the state equation of the systems is derived. Necessary and sufficient conditions for the positivity of fractional descriptor linear discrete-time systems are established. The discussion is illustrated with numerical examples.

scholarly journals Positive 2D Discrete-Time Linear Lyapunov Systems

2009 ◽  
Vol 19 (1) ◽  
pp. 95-106 ◽  
Author(s):  
Przemysław Przyborowski ◽  
Tadeusz Kaczorek
Keyword(s):  
Asymptotic Stability ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Numerical Examples ◽  
Necessary And Sufficient ◽  
Time Linear

Positive 2D Discrete-Time Linear Lyapunov SystemsTwo models of positive 2D discrete-time linear Lyapunov systems are introduced. For both the models necessary and sufficient conditions for positivity, asymptotic stability, reachability and observability are established. The discussion is illustrated with numerical examples.

scholarly journals Positive Partial Realization Problem for Linear Discrete-Time Systems

2007 ◽  
Vol 17 (2) ◽  
pp. 165-171 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Impulse Response ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Finite Sequence ◽  
Realization Problem ◽  
Numerical Examples ◽  
Discrete Time Systems ◽  
Time Systems

Positive Partial Realization Problem for Linear Discrete-Time SystemsA partial realization problem for positive linear discrete-time systems is addressed. Sufficient conditions for the existence of its solution are established. A procedure for the computation of a positive partial realization for a given finite sequence of the values of the impulse response is proposed. The procedure is illustrated by four numerical examples.

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