Zeno-free event-triggered fixed-time control of two-time-scale systems by Chang transformation and backstepping design

This paper investigates fixed-time stabilization of linear two-time-scale systems. The existing fixed-time control techniques are no longer applicable due to the inherent ill-conditioned numerical issues, which is induced by the time-scale separation of two-time-scale systems when carrying out stability analysis. Alternative challenge is that the considered systems are not fully actuated, such that some full rank conditions regarded to the control matrix do not hold anymore. All of these pose difficulties to the fixed-time controller design and stability analysis. To handle these issues, appropriate state transformations are proposed to decouple the system into slow and fast subsystems with approximate strict feedback structure. Then, by the backstepping method, a continuous-time controller is designed to achieve fixed-time stabilization. Furthermore, a Zeno-free event-triggered strategy is proposed to reduce the control updates and then a practical stability result of two-time-scale systems is obtained. A numerical simulation is presented to illustrate the effectiveness of the results.