Mixed H2/H∞ control of markovian jump time-delay systems with uncertain transition probabilities

This study addresses the robust stability problem of Markovian jump time-delay systems with mixed H2 and H∞ control and uncertain transition probabilities in the discrete-time domain. The transition probabilities are considered to be uncertain but bounded. By proposing a new Lyapunov functional and applying the free-weighting matrix technique, we design the mode-dependent mixed H2/H∞ controller such that the resultant closed-loop systems possess stochastic stability and are prescribed with H∞ performance indices. These results generalize several results reported in previous literature, which consider the Markovian transition probabilities to be known a priori or partially unknown transition probabilities. Numerical examples and a practical motion control system are presented to illustrate the effectiveness of this technique.