scholarly journals The Equivalence of Datko and Lyapunov Properties for (h,k)-Trichotomic Linear Discrete-Time Systems

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Claudia-Luminiţa Mihiţ ◽  
Mihail Megan ◽  
Traian Ceauşu
Keyword(s):  
Discrete Time ◽  
General Property ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Infinite Dimensional ◽  
Discrete Time Systems ◽  
Exponential Trichotomy ◽  
Necessary And Sufficient ◽  
Time Systems

The aim of this paper is to characterize a general property of(h,k)-trichotomy through some Lyapunov functions for linear discrete-time systems in infinite dimensional spaces. Also, we apply the results to illustrate necessary and sufficient conditions for nonuniform exponential trichotomy and nonuniform polynomial trichotomy.

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 Fractional descriptor standard and positive discrete-time nonlinear systems

2015 ◽  
Vol 63 (3) ◽  
pp. 651-655
Author(s):  
T. Kaczorek
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Linear Part ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Numerical Example ◽  
Discrete Time Systems ◽  
Necessary And Sufficient ◽  
Time Systems

AbstractA method of analysis of the fractional 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 a numerical example.

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