Stabilisation bound of stochastic singularly perturbed systems with markovian switching by noise control

This study considers the stabilisation-bound problem of stochastic singularly perturbed systems with Markovian jump parameters. The aim of this study is to determine whether a stochastic state-feedback controller referred to be noise control can stabilise such a system for any perturbation parameter ε ϵ (0, ε̅] with a predefined positive scalar ε̅. By introducing an ε-dependent Lyapunov function, new stabilisation method via an ε-dependent controller only in the diffusion part is developed, whose condition independent of ε is within LMI framework. Based on this, more extensions to transition probability matrix with elementwise bounded uncertainties, being partially unknown and system state partially observable are considered, respectively. A numerical example is used to demonstrate the effectiveness and advantage of the proposed methods.