Stability and attractivity in pessimistic value for uncertain dynamical system

The pessimistic value of uncertain variables is a critical value to deal with optimization problems in environments with uncertainty. In many uncertain decision problems, pessimistic values at a certain level of reliability sometimes get attention, such as the problem that the objective function is time or cost. This article introduces two definitions of pessimistic value stability and attractivity. And the corresponding judgment conditions of attractivity are presented for linear differential systems with uncertainty. Furthermore, pessimistic value stability is analyzed for three kinds of nonlinear uncertain differential systems. Then pessimistic value attractivity is considered for a kind of nonlinear differential system with uncertainty.