Robust Fuzzy Model-Based $$H_2/H_\infty$$ Control for Markovian Jump Systems with Random Delays and Uncertain Transition Probabilities

Abstract

This paper studies the mixed \(H_2/H_\infty\) control for Takagi–Sugeno (T–S) fuzzy Markovian jump systems (MJSs) subject to random delays and multiple uncertain transition probabilities. In contrast to existing research, this study presents uncertainty parameters, external disturbance, random delays, and uncertain transition probabilities simultaneously in a unified T–S fuzzy model. Specifically, this study examines multiple Markov chains with partially unknown transition probabilities. These complex imperfections have a substantial adverse impact on system performance and the associated challenge of mixed \(H_2/H_\infty\) control remains unresolved. Our innovative contributions are described as follows. The proposed approach utilizes free-weighting matrix technique and Lyapunov–Krasovskii functional to get the \(H_2/H_\infty\) controller, which ensures that the stochastic T–S fuzzy systems exhibit stochastic stability and comply with the \(H_\infty\) performance index.