It is proven that the solution of the nonlinear complementarity problem is an asymptotically stable equilibrium point of the proposed differential system.

By applying impulsive control theory of the universal equation, the asymptotically stable condition of impulsive control on chaotic attractors in such nonlinear chaotic system was deduced, and with it, the upper bond of the impulse interval for asymptotically stable control was given.

It is proved that the solution of the P0 function complementarity problem is an asymptotically stable equilibrium point of the proposed differential system.

A necessary and sufficient condition for asymptotic stability of first order delay equation with two delays;

A necessary and sufficient condition for asymptotic stability of first order delay equation with two delays

Algebraic criterion for asymptotic stability of first order delay equation with two delays

Under cyclic switching,the stability of a class of discrete time linear switched systems with state delays in subsystems and the specification of dwell time of the subsystems are studied.

Furthermore,a theory including formulaes of resistance identification is used in describing adaptive robust L2 robust controller is obtained by defining storage function,the L2 robust control law which met disturbance restraint and asymptotical stability was proved.

On exponentially asymptotical stability of two dimensional linear differential with periodic coefficient;

The analyses to the energy functions suggest that the proposed model can reach asymptotical stability.