Exponential (Ξ1,Ξ2,γ)$$ \left({\Xi}_1,{\Xi}_2,\gamma \right) $$‐Dissipative Synchronization of Quaternion‐Valued Nonlinear Differential Systems With Multiple Time‐Varying Leakage Delays

ABSTRACT This paper studies the exponential ‐dissipative synchronization control problem of quaternion‐valued nonlinear delayed differential systems (NDDSs). The types of delays considered time‐varying leakage, distributed and transmission delays. First, an inequality related to solutions of the error system is established. Then, an easy‐to‐implement state‐feedback controller is constructed to obtain an exponential ‐dissipative synchronization criterion. Furthermore, an algorithm is proposed to solve the nonlinear terms in the obtained criterion. Finally, the effectiveness of the derived results is demonstrated by two numerical examples. It is worth emphasizing that the exponential ‐dissipative synchronization control problem for quaternion‐valued NDDSs under consideration is addressed for the first time.