State Based Self-triggered Feedback Control Systems with ℒ2 Stability

Abstract

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 by Lemmon et al. (2007) 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 ℒ2 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∞ 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.