The mean-square exponential stability and instability of stochastic nonholonomic systems

We present a new methodology for studying the mean-square exponential stabi lity and instability of nonlinear nonholonomic systems under disturbance of Gaussian white-noise by the first approximation. Firstly, we give the line arized equations of nonlinear nonholonomic stochastic systems; then we cons truct a proper stochastic Lyapunov function to investigate the mean-square exponential stability and instability of the linearized systems, and thus d etermine the stability and instability in probability of corresponding comp eting systems. An example is given to illustrate the application procedures .