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 epsilon is an element of(0, (epsilon) over bar epsilon] with a predefined positive scalar (epsilon) over bar. By introducing an epsilon-dependent Lyapunov function, new stabilisation method via an epsilon-dependent controller only in the diffusion part is developed, whose condition independent of epsilon 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.