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Stability Analysis of Distributed-Order Systems: a Lyapunov Scheme

This paper introduces a novel Lyapunov-based method for stability analysis of distributed-order systems with different fractional-order weight functions in their pseudo-states' dynamics and in the presence of time-delay. First, stability analysis of the integer-order counterparts of the distributed order systems are considered. Under some circumstances, the proposed stability analysis method is extended for distributed-order systems. The proposed method is not limited to the distributed-order ordinary differential equations and can be applied to the distributed-order partial differential equations, too. In fact, the proposed stability analysis method links stability of distributed-order systems to the stability of their integer-order counterparts. Evaluation of the above-mentioned achievements are done by two numerical examples.