Abstract
This paper proposes a new method of getting Lyapunov functions using randomization, state discretization, and quantization of the Markov process. We deal with continuous deterministic systems as discrete stochastic systems and quantize the systems. The randomization of deterministic systems is introduced because we are aiming at the extension of the method to the stable stochastic case in future works. This procedure introduces Schrödinger-like equations. The problem of obtaining Lyapunov functions is replaced by the problem of solving eigen equations of the Schrödinger-like equations. In previous works of obtaining Lyapunov functions, for example, Fleming and Soner's method, there is the case that numerical approximated values diverge because of iteration of calculation. However, our method does not cause the problem because it is based on eigen analysis.
