$${\mathscr {H}}_2$$ H 2 and $${\mathscr {H}}_\infty $$ H ∞ State-Feedback Control for Discrete-Time Markov Jump Lur’e Systems

We propose LMI conditions for $${\mathscr {H}}_2$$ and $${\mathscr {H}}_\infty $$ analysis and state-feedback control of discrete-time Markov jump Lur’e systems. We also consider two possible approaches, either mode-dependent or mode-independent state-feedback control. We assume that the Markov mode $$\theta (k)$$ is available to the controller for the first case, and for the second one, the random variable is not available to the controller. A numerical example illustrates the obtained results.