Mixed H₂/H_∞ stabilization design for memristive neural networks

This study considers the multiobjective stabilization design problem for memristive neural networks (MNNs). Initially, by using a set of logical switched functions, the original MNN is transformed into another model which is easy to be dealt with. Then, based on the transformed model and using the Lyapunov direct method, a mixed H₂/H_∞ control design is developed in the form of linear matrix inequalities (LMIs), such that the closed-loop MNN is exponentially stable and an H₂ performance bound is given while providing a prescribed H_∞ performance of disturbance attenuation. Furthermore, via the existing LMI optimization technique, a suboptimal mixed H₂/H_∞ controller can be constructed in the sense of making the H₂ performance bound as small as possible. Finally, numerical simulations exhibit the feasibility and validity of the proposed design method.