Robust stochastic stability and delayed-state-feedback stabilisation of uncertain Markovian jump linear systems with random time delays

The problem of robust stochastic stability and delayed-state-feedback stabilisation of uncertain Markovian jump linear systems with random Markov delays is investigated. Based on the Lyapunov stability theory and robust analysis techniques, some robust stochastic stability criteria are derived in terms of linear matrix inequalities. Robust delayed-state-feedback controllers that stochastically stabilise the uncertain Markovian jump linear systems is also proposed. The state variable on the controller is assumed to be dependent on the Markov delay that has uncertain transition probabilities. Finally, numerical examples are provided to illustrate the feasibility and effectiveness of the proposed methods.