Stochastic Nonlinear Control Stablizability Based on Invers Optimality

  The main aim of this work is focused on studying the global asymptotic stability in the probability for some class of closed-loop control system of Itotype in the presence of system uncertainty.  Some onlinear continuous-time Ito-dynamic stochastic system deriven by unbounded stochastic noise input have been considered, where the equilibrium point of the stochastic system is preserved even in the presence of noise  The global asymptotic stability in probability has been developed by using stabilization controller and Lyapunov stochastic approach. The stochastic Lyapunov function is computed to guarantee the global asymptotic stability in probability. Some resulte of estimation of exponential stability is also discussed.  The necessary theorem for finding the controller design and stability Lyapunov
stochastic function have been stated and proved which are supported by some concluding remarks and illustrations.