Study on the dynamic behavior of planar switched systems near the switching boundary
二阶切换系统在切换线附近的动态行为研究

The conception of approaching region and leaving region of the switching boundary is developed. The sufficient conditions that the sliding mode occurs along the switching boundary and the stability of the sliding mode are obtained. Meanwhile the sufficient conditions that the sliding mode does not occur are given. Under the assumption of the switching delay time being positive, the sufficient conditions that the quasi-sliding mode occurs along the switching boundary are proposed. Some numerical simulations validate the main results.