连续线性切换系统的镇定慢切换设计

针对含有两个不稳定子系统的线性切换系统,设计一种包含时间驱动和状态驱动两个环节的切换法则,使线性切换系统稳定.在该切换法则下,系统的类Lyapunov函数在两个环节都不需要严格单调递减,使得系统在每个子系统有更长的驻留时间,从而有效降低系统的切换频率.在适当的假设条件下,带时变扰动的线性切换系统在该切换信号下具有良好的鲁棒稳定性.基于此,当系统可观测时,进一步设计了基于观测器的混合切换法则,实现了系统的鲁棒稳定.

Stabilizing slow-switching strategy for continuous-time switched linear systems

By combining a time-driven mechanism with a state-driven mechanism, a new switching strategy is designed to stabilize the switched linear systems with two unstable subsystems. Under this strategy, the Lyapunov-like function of the system is not necessary to be decreasing in both time-driven and state-driven mechanisms, which permits the subsystems to have a longer dwell-time to reduce the switching frequency remarkably. For suitable assumptions on the system dynamics, the system with time-varying disturbances has a good robust stability under the designed switching strategy. Moreover, when the system is observable, an observer-based combined switching law is designed, which robustly stabilizes the perturbed systems.