Perspectives and results on the stability and stabilizability of hybrid systems

This paper introduces the concept of a hybrid system and some of the challe nges associated with the stability of such systems, including the issues of guaranteeing stability of switched stable systems and finding conditions f or the existence of switched controllers for stabilizing switched unstable systems. In this endeavor, this paper surveys the major results in the (Lya punov) stability of finite-dimensional hybrid systems and then discusses th e stronger, more specialized results of switched linear (stable and unstabl e) systems. A section detailing how some of the results can be formulated a s linear matrix inequalities is given. Stability analyses on the regulation of the angle of attack of an aircraft and on the PI control of a vehicle w ith an automatic transmission are given. Other examples are included to ill ustrate various results in this paper.