Stability and l2-gain analysis for a class of discrete-time non-linear Markovian jump systems with actuator saturation and incomplete knowledge of transition probabilities

This study deals with the control problems of a class of discrete-time non-linear Markovian jump systems subject to saturating actuators and incomplete knowledge of transition probabilities. Modal non-linearities satisfying sector conditions are taken into consideration. Sufficient conditions that guarantee the closed-loop system to be locally stochastically stable are given. The linear matrix inequality (LMI) approach is used to analyse the closed-loop plant stability and l₂-gain. Conditions in terms of LMIs are provided for obtaining an l₂-gain as small as possible. A simulation example is given to illustrate the effectiveness of the proposed method.