scholarly journals Study onH-Index of Stochastic Linear Continuous-Time Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Yan Li ◽  
Tianliang Zhang ◽  
Xikui Liu ◽  
Xiushan Jiang
Keyword(s):  
Continuous Time ◽  
Necessary And Sufficient Condition ◽  
Continuous Time Systems ◽  
Generalized Differential Equation ◽  
Generalized Differential ◽  
Necessary And Sufficient ◽  
Index Problem ◽  
Time Systems ◽  
Detection Filter ◽  
Filter Analysis

This paper studies theH-index problem. We obtain a necessary and sufficient condition ofH-index larger thanγ>0. A generalized differential equation is introduced and it is proved that its solvability and the feasibility of theH-index are equivalent. We extend the deterministic cases to the stochastic models. Our results can be used to fault detection filter analysis. Finally, the effectiveness of the proposed results is illustrated by an example.

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 Computation of positive realizations for descriptor linear continuous-time systems

2018 ◽  
Vol 19 (12) ◽  
pp. 428-432
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
New Method ◽  
Transfer Matrices ◽  
Continuous Time Systems ◽  
Necessary And Sufficient ◽  
Time Systems ◽  
Time Linear

A new method for computation of positive realizations of given transfer matrices of descriptor linear continuous-time linear systems is proposed. Necessary and sufficient conditions for the existence of positive realizations of transfer matrices are given. A procedure for computation of the positive realizations is proposed and illustrated by 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.

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