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This paper addresses the problem of global μ -stability for quaternion-valued neutral-type neural networks (QVNTNNs) with time-varying delays. First, QVNTNNs are transformed into two complex-valued systems by using a transformation to reduce the complexity of the computation generated by the non-commutativity of quaternion multiplication. A new convex inequality in a complex field is introduced. In what follows, the condition for the existence and uniqueness of the equilibrium point is primarily obtained by the homeomorphism theory. Next, the global stability conditions of the complex-valued systems are provided by constructing a novel Lyapunov–Krasovskii functional, using an integral inequality technique, and reciprocal convex combination approach. The gained global μ -stability conditions can be divided into three different kinds of stability forms by varying the positive continuous function μ ( t ) . Finally, three reliable examples and a simulation are given to display the effectiveness of the proposed methods.

This paper focuses on the exponential stabilization problem for Markov jump neural networks with Time-varying Delays (TDs). Firstly, we provide a new Free-matrix-based Exponential-type Integral Inequality (FMEII) containing the information of attenuation exponent, which is helpful to reduce the conservativeness of stability criteria. To further save control cost, we introduce a sample-based Adaptive Event-triggered Impulsive Control (AEIC) scheme, in which the trigger threshold is adaptively varied with the sampled state. By fully considering the information about sampled state, TDs, and Markov jump parameters, a suitable Lyapunov–Krasovskii functional is constructed. With the virtue of FMEII and AEIC scheme, some novel stabilization criteria are presented in the form of linear matrix inequalities. At last, two numerical examples are given to show the validity of the obtained results.