Viability Decision For A Solution Of Differential System

Viability theory describes the relationship between the dynamic and the constraint of system via differential inclusions, uses set-valued analysis studying the evolution of system and reveals the potential regulatory feedback. Viability theory offers mathematical method of evolution of macrosystems arising in biology, economics, and society. In the second chapter,we introduce some viability theorem of the deterministic differential system at first, and then we discuss the viability of the deterministic differential in case of control factors.At last we introduce the viability condition for an affine nonlinear control system in a kind of non-smooth region defined by subdifferential functions. This verification can be implemented by determining the consistency of a group of linear inequalities, or equivalently,by solving a linear programming problem. In the third chapter, we devote to viability theorem of stochastic differential system.Then we give sufficient condition for viability of stochastic differential system described by Lyapunov function.The new result will be illustrated by many examples.