Stability of delayed quaternion-valued singular systems with Markov switching

In this paper, the stability problem of delayed quaternion-valued singular systems with Markov switching is investigated. By constructing an appropriate Lyapunov-Krasovskii functional and employing matrix inequality techniques, sufficient conditions are derived in the form of quaternion-valued linear matrix inequalities to ensure the stability of the closed-loop system, and the state feedback controller is designed. Two illustrative examples and corresponding simulations are also provided to verify the effectiveness of the proposed theoretical results.