Lyapunov conditions for the finite-time stability of fractional order disturbed nonlinear systems and neural networks: The secure image communication using encryption

Abstract

Certain Lyapunov conditions for the finite-time stability (FTS) and global FTS of a general nonlinear disturbed fractional ordered system is established initially. A settling time depending on the initial conditions of the system is introduced ensuring the FTS of the system and the result is then extended to global FTS. Secondly, FTS of a fractional ordered nonlinear disturbed neural network is examined using a linear matrix inequality (LMI). Finally, a few examples are depicted to validate the established results. Further, the models are extended to design novel image encryption algorithms based on FTS, which is seen to be more efficient than the existing methods. The qualitative and quantitative results proves that the models performed well with images and ensured secure communication between sender and receiver.