Construction Method of Approximate Stochastic Lyapunov Functions using Quantization of Markov Process

Abstract

The existence of stochastic Lyapunov functions assures that the systems are stable in probability. However, general scheme of obtaining stochastic Lyapunov functions has not been introduced yet. This paper extends the authors’ previous method[21] obtaining Lyapunov functions for deterministic cases to stochastic cases. In the method, difference-approximation scheme[6,10] and quantization of Markov processes[1,14] are used to approximate Lyapunov equations by linear quantum-like equations. We propose a method of obtaining approximate stochastic Lyapunov functions for nonlinear stochastic systems by superimposing the eigenfunctions of the quantum-like equations.