Stability of delayed quaternion-valued neural networks with general probabilistic bounded Markovian switching

The study delves into the stability problem of quaternion-valued neural networks (QVNNs) with time-varying discrete delays and distributed delays as well as general probabilistic bounded Markovian switching. Firstly, the non-commutative nature of quaternion multiplication complicates theoretical analysis and numerical computation when decomposition methods are employed. To address this, a suitable Lyapunov-Krasovskii functional is constructed and combined with the method of free-weighting matrix and inequality techniques, the QVNNs with Markovian switching are analyzed as a whole, yielding stability criteria in the form of linear matrix inequalities (LMIs). Additionally, as the transition probabilities are general probabilistic bounded, the system becomes more versatile and realistic. Finally, two example with simulations are given to show the validity and applicability of the achieved result.