Finite-Time Synchronization of Fractional-Order Nonlinear Systems with State-Dependent Delayed Impulse Control
Gokul P. Mohanrasu S.S. Kashkynbayev A. Rakkiyappan R.
15 March 2024World Scientific
International Journal of Bifurcation and Chaos
2024#34Issue 3
This paper delves into the topics of Finite-Time Stabilization (FTS) and Finite-Time Contractive Stabilization (FTCS) for Fractional-Order Nonlinear Systems (FONSs). To address these issues, we employ a State-Dependent Delayed Impulsive Controller (SDDIC). By leveraging both Lyapunov theory and impulsive control theory, we establish sufficient conditions for achieving stability criteria for fractional-order systems. Initially, we employ the aforementioned sufficient conditions to derive stability criteria for general FONSs within the SDDIC framework, employing Linear Matrix Inequality (LMI) techniques. Furthermore, we apply these theoretical findings to tackle the challenge of finite-time synchronization in fractional-order chaotic systems using the proposed SDDIC. We substantiate the efficacy of these theoretical advancements through numerical simulations that vividly demonstrate their capability to achieve finite-time synchronization in fractional-order cellular neural networks and fractional-order Chua’s circuits. Moreover, we introduce an innovative chaos-based multi-image encryption algorithm, thereby contributing significantly to the field. To ensure the algorithm’s robustness, we subject it to rigorous statistical tests, which confidently affirm its capacity to provide the requisite level of security.
Chua’s circuit , fractional-order system , image encryption , impulsive control , linear matrix inequality , Stabilization
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Department of Mathematics, Bharathiar University, Tamil Nadu, Coimbatore, 641 046, India
Department of Mathematics, Nazarbayev University, Nur-Sultan City, Kazakhstan
Department of Mathematics
Department of Mathematics
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