Introduction

Abstract

Generally speaking, the stability analysis of the system is one of the key research problems of the system, which needs to be solved in both system analysis and control system design. In practical systems, such as the chemical industry and metallurgy, launch vehicles, space shuttles, and power grids, due to aging components, environmental changes, insensitive measurement or signal transmission, the system is often affected by time delays, parameter uncertainties, external interference, random noise, and other factors. In the presence of these unstable factors, its stability analysis becomes particularly critical. In the past 100 years, the stability analysis of various systems, especially nonlinear time delayed systems, has received extensive attention and in-depth discussion from scholars. At 4:40 p.m. on April 26, 1982, CAAC flight 3303 226 from Guangzhou to Guilin crashed over Gongcheng, 45 km away from Guilin. A total of 112 passengers and 8 crew members were killed. The reason was that the aircraft rolled due to an autopilot failure. When the roll reached 45 degrees, the pilot noticed the instrument, but at this time, the instrument display was misinterpreted. The pilot continued to press the bar to increase the roll, and finally rolled to 180 degrees, and the nose hit the mountain downward. On March 23, 2005, the isomerization unit of British Petroleum Company in Texas refinery exploded, which was caused by the malfunction of the liquid level gauge at the bottom of the tower.