Stabilization Of Switched Systems Based On Sampled Feedback

Hybrid system is a combination of discrete and continuous dynamical systems. A switched system is a class of hybrid system composed of several dynamical subsystems and a switching law that specifies the active subsystem at each instant of time. The nature of switched systems is switching, however it is not the sample addition of those of different subsystems and has some particularity and complexity. In recent years, many people pay attention to switch system and in-depth research and gained a lot of achievements, especially in its stability. There are many perfect results on the stability of switching systems.Most practical systems are continuous in nature but with discrete (sampled) feedback. Based on the basic concepts and methods of control theory, with the help of proper mathematics tools, stabilization of switched continuous-time systems based on sampled feedback and the possibility of its practical application are investigated.The system under consideration is assumed to experience model switching consistently with known or unknown switching process. On the basis of stability theory, we obtain the sufficient conditions for stability about Dwell times and the sampling period. When the switching signal cannot observe, it is shown that by combining on-line adaptive estimation with sampled feedback control, the system is ensured to be globally stable.The paper is organized as follows:In the first section:It is assumed that the linear systems model switches among an infinite set of uniformly controllable linear systems and the switched signals are known, but the switching duration has a lower bound, a sampled feedback control law can be constructed which makes the switched linear system globally stable. The result is illustrated by a simulation example.In the second section:When the switching signal is unknown and tk/h is an integer, it will be shown that by combining on-line adaptive estimation and control in the controller design, a sampled feedback control law can be constructed which makes the switched linear system globally stable. The result is illustrated by a simulation example. In the third section:When the switching signal is unknown and tκ/h is not an integer, to address the situation of unknown switching model, we first identify the switching signal at the beginning of each time interval, and then control the identified system in the rest of the time in the interval.In the forth section:Validation and verification of the established result is conducted through cruise control of high speed train.In the fifth sectionConclude the research work of this paper.