Asynchronous mode‐dependent sampled‐data control of non‐homogeneous Markovian jump linear systems via an improved looped‐functional approach

Abstract

Abstract This paper investigates the asynchronous mode‐dependent sampled‐data control synthesis for non‐homogeneous Markovian jump systems subject to generalised transition rates and bounded conditional probabilities. To increase the reality in system modelling, the asynchronous phenomenon between plant mode and sampled plant mode (i.e. control mode) is explored along with the non‐homogeneous nature of the Markov process, and the time variability of the conditional probabilities indicating the degree of the asynchronous phenomenon is imposed on the stabilisation process. Moreover, to achieve less conservative results, a reinforced looped‐functional is established by introducing two novel time‐integrated states, so that more detailed state information can be utilised during the stabilisation process, and an effective relaxation technique is proposed so that the zero‐sum and boundary constraints of multiple time‐varying parameters can be sufficiently utilised when transforming the parameterised stabilisation conditions into linear matrix inequalities.