Multiple event‐triggered schemes for a class of switched descriptor systems with asynchronous switching

Abstract

This article studies asynchronous switching for a class of switched descriptor systems (SDSs) under multiple event-triggered schemes (ETSs). First, by using a mode-dependent coordinates transformation, a SDS is equivalently transformed into a reduced-order ordinary switched linear system with state jumps. Then, multiple ETSs are used to transmit the state and switching signal information. The asynchronism between system modes and controller modes inevitably happens in a switching interval. Next, by constructing a controller-mode-dependent Lyapunov functional and using the asynchronous switching strategy, an exponential stability criterion is presented for the closed-loop system with average dwell time switching signals. Meanwhile, the state feedback controller and multiple ETSs are codesigned. Besides, the Zeno behavior is avoided. In the end, the validity of the proposed method is demonstrated by a numerical example.

Composite event‐triggered H∞ control for nonlinear switched singular systems with a mode‐dependent triggering strategy

“…The traditional ETSs are always framed based on the fact that the states are continuous, while for discontinuous systems, these methods may be ineffective. Thus, in References 8,45,46, the hybrid mode‐dependent ETS introduced a positive constant related to the minimum dwell time to eliminate the Zeno behavior. However, in a practical switched system, it's not easy to obtain the exact minimum residence time, because the dwell time sequence is randomly generated.…”

“…However, in a practical switched system, it's not easy to obtain the exact minimum residence time, because the dwell time sequence is randomly generated. Moreover, as discussed in References 8,45,46, when SSs switch from one mode to another but the event is not triggered, the asynchronous switching occurs, which can damage the stability. Inspired by Li et al, 47 Lyapunov function is introduced into ETS (11) to overcome this drawback.…”

“…In Reference 44, the ETS was primarily based on the controller error rather than the general state error, and the system tracking error was treated as a constant threshold to exclude Zeno behavior. In References 8,45,46, multiple ETSs consisting of mode‐dependent ETSs and minimum‐dwell‐time‐dependent ETSs were applied to the stabilization problems of SSs/SSSs. Nevertheless, these ETSs either do not apply to SSSs or ignore the fact that event‐triggered sampling may cause asynchronous phenomena in the SSs.…”

“…The principal contributions are listed below: A novel hybrid event‐triggered controller containing a feedback controller and an impulsive controller is constructed. This controller can effectively suppress the impulse effects at the switching instant while ensuring the performance of event‐triggered sampling even if each subsystem is unstable. Different from the minimum‐dwell‐time‐dependent hybrid ETSs in References 8,45,46, two novel classes of ETSs are simultaneously merged into a mode‐dependent hybrid ETS. In the first class of sub‐ETSs, the disturbance term plays an active role as a non‐negative threshold, which effectively excludes the Zeno behavior.…”

Asynchronously H∞ Tracking Control and Optimization for Switched Flight Vehicles with Time-Varying Delay

“…The results in the paper validate that asynchronous switching can affect the system's dynamic performance, and it is essential to avoid the undesirable response induced by asynchronous switching. Moreover, the multiple event-triggered strategies for switched systems with asynchronous switching were investigated in [21]. The controller-mode-dependent Lyapunov function was established using an asynchronous switching strategy.…”