Stochastic Asymptotic Stabilizers for Deterministic Input-Affine Systems   based on Stochastic Control Lyapunov Functions
  In this paper, a stochastic asymptotic stabilization method is proposed for deterministic input-affine control systems, which are randomized by including Gaussian white noises in control inputs. The sufficient condition is derived for the diffucion coefficients so that there exist stochastic control Lyapunov functions for the systems. To illustrate the usefulness of the sufficient condition, the authors propose the stochastic continuous feedback law, which makes the origin of the Brockett integrator become globally asymptotically stable in probability. 
Yuki Nishimura, Kanya Tanaka, Yuji Wakasa and Yuh Yamashita
math.OC