Dissipative and dissipativity analysis for quaternion-valued fractional-order discrete-time memristive neural networks

This paper illustrates the dissipative and dissipativity analysis for the fractional-order memristive system with quaternion terms. The purpose is to derive some conditions that are capable of guaranteeing the stability and dissipativity of the system. By resorting to a novel functional, sufficient conditions for the solvability of the above problem are established in the form of algebraic inequality and linear matrix inequality (LMI). In addition, based on the linear fractional difference system, the dissipativity conclusion is obtained, in which, the globally attractive sets is figured out as well. Finally, three examples are given to show the application of our proposed methods.