Self-Triggered Feedback Control Systems With Finite-Gain ${cal L}_{2}$ Stability

This paper examines a class of real-time control systems in which each control task triggers its next release based on the value of the last sampled state. Prior work used simulations to demonstrate that self-triggered control systems can be remarkably robust to task delay. This paper derives bounds on a task´s sampling period and deadline to quantify how robust the control system´s performance will be to variations in these parameters. In particular we establish inequality constraints on a control task´s period and deadline whose satisfaction ensures that the closed-loop system´s induced L ₂ gain lies below a specified performance threshold. The results apply to linear time-invariant systems driven by external disturbances whose magnitude is bounded by a linear function of the system state´s norm. The plant is regulated by a full-information H _infin controller. These results can serve as the basis for the design of soft real-time systems that guarantee closed-loop control system performance at levels traditionally seen in hard real-time systems.