Stabilisation of hybrid stochastic systems by disordered controllers

Abstract

This study considers the stabilisation problem of hybrid stochastic systems by regular and stochastic state feedback controllers whose operation modes suffer a disordering phenomenon. By introducing an augmented Markov chain, a new operation mode is used to describe such a disagreement. Without designing a controller with new operation mode directly, a kind of controllers only having original operation mode is developed by using the non-fragile control method, whose condition is given as linear matrix inequalities with equation constraints. Moreover, extensions to transition probability matrix with elementwise bounded uncertainties and being partially unknown are obtained. Simulation examples are used to demonstrate the effectiveness of the proposed methods.