Generalised admissible stability and synchronisation of distributed-order nonlinear singular systems via Wright function approach

This paper addresses the admissible stability analysis of distributed-order nonlinear singular systems by proposing two novel stability criteria. First, an asymptotic stability condition is established for the approximated multi-term system associated with the original distributed-order model by extending existing results to the singular setting via Laplace transform techniques tailored for distributed-order dynamics. Second, a generalised Wright stability criterion is developed, which provides a unified framework that captures both classical asymptotic and Mittag–Leffler stability as special cases, thereby offering a more comprehensive characterisation of system behaviour. As an application, we propose for the first time a synchronisation scheme for a class of coupled distributed-order singular systems, thereby demonstrating the practical significance and applicability of the developed theoretical framework. The effectiveness of the proposed results is illustrated through three numerical examples with supporting simulations.