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Exponential synchronization for variable-order fractional discontinuous complex dynamical networks with short memory
Ruihong Li1, Huaiqin Wu1, Jinde Cao2
1School of Science, Yanshan University, Qinhuangdao 066001, China.
Summary
This study addresses exponential synchronization for discontinuous variable-order fractional complex dynamical networks using an impulsive control scheme. The research develops a novel hybrid controller and synchronization conditions for enhanced network stability and control.
Area of Science:
- Control Theory
- Nonlinear Dynamics
- Fractional Calculus
Background:
- Complex dynamical networks are crucial in modeling various systems.
- Fractional-order systems offer enhanced modeling capabilities.
- Discontinuous systems present unique control challenges.
Purpose of the Study:
- To investigate exponential synchronization in variable-order fractional complex dynamical networks (FCDNs) with short memory and derivative couplings.
- To develop a robust impulsive control scheme for these complex systems.
- To design a hybrid controller integrating impulsive and discontinuous feedback control.
Main Methods:
- Establishing a mathematical model for variable-order fractional systems with short memory under impulsive control.
- Developing an exponential stability criterion for these systems.
- Designing a hybrid controller comprising impulsive coupling and discontinuous feedback control.
- Utilizing Lyapunov functional construction and inequality analysis.
- Formulating synchronization conditions in terms of linear matrix inequalities (LMIs).
Main Results:
- A novel mathematical model for FCDNs with short memory and discontinuous nodes under impulsive control.
- An exponential stability criterion tailored for variable-order fractional systems.
- Successful design of a hybrid controller for synchronization.
- Derivation of synchronization conditions expressed as LMIs.
- Validation of the proposed synchronization scheme through simulation examples.
Conclusions:
- The developed impulsive control scheme effectively achieves exponential synchronization in variable-order FCDNs.
- The hybrid controller and derived LMI conditions provide a reliable method for controlling discontinuous complex dynamical networks.
- Simulation results confirm the theoretical findings and the practical applicability of the proposed synchronization strategy.
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