Stochastic Lyapunov function design using quantization of Markov process

We propose a new procedure for designing approximate stochastic Lyapunov functions (SLFs) for nonlinear Ito stochastic systems. We approximate nonlinear stochastic Lyapunov equations (SLEs) by linear Schrodinger-like equations with Kushner¿s scheme of difference approximation and Alcaraz et al.¿s ¿quantization of Markov processes.¿ We construct time-invariant functions concerned with the solutions of Schrodinger-like equations and then obtain sufficient conditions for converting the time-invariant functions into approximate SLFs.