The braid group is infinite non-commutative group, and it has many hard problems that can be utilized to design cryptographic primitives, such as the word problem, conjugacy problem and root problem.

A non - affine nonlinear model for a single - machine infinite - bus system with static VAR compensator SVC is established.

Besides, our paper has discussed another problem, which is the non - exponential stability of infinite - dimensional linear systems under generating compact perturbation.