Perspectives and results on the stability and stabilizability of hybrid systems

Author

DeCarlo, Raymond A. ; Branicky, Michael S. ; Pettersson, Stefan ; Lennartson, Bengt

Author_Institution

Dept. of Electr. Eng., Purdue Univ., West Lafayette, IN, USA

Volume

88

Issue

7

fYear

2000

fDate

7/1/2000 12:00:00 AM

Firstpage

1069

Lastpage

1082

Abstract

This paper introduces the concept of a hybrid system and some of the challenges associated with the stability of such systems, including the issues of guaranteeing stability of switched stable systems and finding conditions for the existence of switched controllers for stabilizing switched unstable systems. In this endeavour, this paper surveys the major results in the (Lyapunov) stability of finite-dimensional hybrid systems and then discusses the stronger, more specialized results of switched linear (stable and unstable) systems. A section detailing how some of the results can be formulated as 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 with an automatic transmission are given. Other examples are included to illustrate various results in this paper.

Keywords

Lyapunov methods; control system analysis; discrete systems; matrix algebra; multidimensional systems; stability; two-term control; Lyapunov stability; PI control; aircraft angle-of-attack regulation; automatic transmission; finite-dimensional hybrid systems; guaranteed stability; hybrid systems; linear matrix inequalities; stability analysis; stabilizability; switched linear systems; switched stable systems; switched unstable systems; vehicle; Aircraft; Automata; Control systems; Decision making; Difference equations; Linear matrix inequalities; Pi control; Stability analysis; Switched systems; Vehicles;

fLanguage

English

Journal_Title

Proceedings of the IEEE

Publisher

ieee

ISSN

0018-9219

Type

jour

DOI

10.1109/5.871309

Filename

871309