Semi-Global Bounded Output Regulation of Linear Two-Time-Scale Systems With Input Saturation

Standard output regulation design techniques cannot be applied for linear two-time-scale systems subject to saturated inputs. In this work, a state feedback output regulation is first proposed based on a classical stabilizing composite state feedback controller. Nevertheless, the corresponding design is difficult to implement due to numerical issues. Thus, the method of asymptotic power series expansion is applied to provide an approximate solution to the regulator equation. Then, a time-continuous state feedback controller is designed by combining the Chang transformation approach and the low-gain feedback technique, which results in a semi-global bounded output regulation of the closed-loop system. Furthermore, to reduce control updates, a dynamic event-triggered control scheme is proposed which ensures the exclusion of Zeno behavior by maintaining a strictly positive time between any two triggering moments, regardless of the initial state of the system. Additionally, an observer-based event-triggered control scheme is proposed to cater to the practical scenario in which system state information is unavailable. Finally, to demonstrate the effectiveness of our proposed technique, two examples are presented.