Robust stability bounds of uncertain fractional-order systems

2014 ◽  
Vol 17 (1) ◽  
Author(s):  
YingDong Ma ◽  
Jun-Guo Lu ◽  
WeiDong Chen ◽  
YangQuan Chen
Keyword(s):  
Fractional Order ◽  
Robust Stability ◽  
Asymptotical Stability ◽  
Asymptotically Stable ◽  
Fractional Order Systems ◽  
Infinity Norm ◽  
Stability Bound ◽  
Bounded Uncertainty ◽  
Theoretical Results

AbstractThis paper considers the robust stability bound problem of uncertain fractional-order systems. The system considered is subject either to a two-norm bounded uncertainty or to a infinity-norm bounded uncertainty. The robust stability bounds on the uncertainties are derived. The fact that these bounds are not exceeded guarantees that the asymptotical stability of the uncertain fractional-order systems is preserved when the nominal fractional-order systems are already asymptotically stable. Simulation examples are given to demonstrate the effectiveness of the proposed theoretical results.

scholarly journals Adaptive - Synchronization of Fractional-Order Chaotic Systems with Nonidentical Structures

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Li-xin Yang ◽  
Wan-sheng He
Keyword(s):  
Adaptive Control ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Control Technique ◽  
Adaptive Synchronization ◽  
Fractional Order Systems ◽  
The Stability ◽  
Different Chaotic Systems ◽  
Theoretical Results

This paper investigates the adaptive - synchronization of the fractional-order chaotic systems with nonidentical structures. Based on the stability of fractional-order systems and adaptive control technique, a general formula for designing the controller and parameters update law is proposed to achieve adaptive - synchronization between two different chaotic systems with different structures. The effective scheme parameters identification and - synchronization of chaotic systems can be realized simultaneously. Furthermore, two typical illustrative numerical simulations are given to demonstrate the effectiveness of the proposed scheme, for each case, we design the controller and parameter update laws in detail. The numerical simulations are performed to verify the effectiveness of the theoretical results.

Topology Identification and Adaptive Synchronization of Fractional-Order Complex Networks

2013 ◽  
Vol 850-851 ◽  
pp. 936-938
Author(s):  
Jin Ping Jia
Keyword(s):  
Complex Networks ◽  
Fractional Order ◽  
Topological Structure ◽  
Adaptive Synchronization ◽  
Fractional Order Systems ◽  
Topology Identification ◽  
Uncertain Network ◽  
Key Space ◽  
System Nodes ◽  
Theoretical Results

This paper investigates topology identification and adaptive synchronization of uncertain complex networks with fractional-order systems nodes. In comparison with those of the integerorder chaotic system nodes, this method is more efficiently which can enlarge the key space. Moreover, the uncertain network topological structure is identified simultaneously in the process of synchronization. Illustrative examples are presented to demonstrate the application of the theoretical results.

scholarly journals Solution of linear fractional order systems with variable coefficients

2020 ◽  
Vol 23 (3) ◽  
pp. 753-763
Author(s):  
Ivan Matychyn ◽  
Viktoriia Onyshchenko
Keyword(s):  
Linear Systems ◽  
Fractional Order ◽  
Initial Value Problem ◽  
Transition Matrix ◽  
State Transition ◽  
Variable Coefficients ◽  
Explicit Solutions ◽  
Fractional Order Systems ◽  
Initial Value ◽  
Theoretical Results

AbstractThe paper deals with the initial value problem for linear systems of FDEs with variable coefficients involving Riemann–Liouville derivatives. The technique of the generalized Peano–Baker series is used to obtain the state-transition matrix. Explicit solutions are derived both in the homogeneous and inhomogeneous case. The theoretical results are supported by an example.

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