Network-Based Robust $\mathscr {H}_{2}/\mathscr {H}_\infty $ Control for Linear Systems With Two-Channel Random Packet Dropouts and Time Delays

This paper focuses on the robust output feedback ℋ₂/ℋ_∞ control issue for a class of discrete-time networked control systems with uncertain parameters and external disturbance. Sensor-to-controller and controller-to-actuator packet dropouts and time delays are considered simultaneously. According to the stochastic characteristic of the packet dropouts and time delays, a model based on a Markov jump system framework is proposed to randomly compensate for the adverse effect of the two-channel packet dropouts and time delays. To analyze the robust stability of the resulting closed-loop system, a Lyapunov function is proposed, based on which sufficient conditions for the existence of the ℋ₂/ℋ_∞ controller are derived in terms of linear matrix inequalities, ensuring robust stochastic stability as well as the prescribed ℋ₂ and ℋ_∞ performance. Finally, an angular positioning system is exploited to demonstrate the effectiveness and applicability of the proposed design strategy.