Qualitative analysis of differential automata: existence and stability of limit cycles

Author

Savkin, Andrey V. ; Matveev, Alexey S.

Author_Institution

Dept. of Electr. & Electron. Eng., Western Australia Univ., Nedlands, WA, Australia

fYear

1999

fDate

1999

Firstpage

265

Lastpage

270

Abstract

We introduce a new class of hybrid dynamical systems. We call these hybrid systems cyclic linear differential automata (CLDA). Our main results show that any CLDA can be reduced to a linear discrete-time system with periodic coefficients. Any CLDA has no singular points. Therefore, the simplest attractor in such systems is a periodic trajectory. We call a CLDA globally stable if it has a periodic trajectory which attracts all other trajectories of this system. A necessary and sufficient condition for global stability of CLDA is given. We apply our result to prove global stability of a flexible manufacturing system modelled as a switched server system. Furthermore, we prove global stability of a class of switched server flow networks

Keywords

automata theory; limit cycles; stability criteria; CLDA; FMS; attractor; cyclic linear differential automata; differential automata; flexible manufacturing system; global stability condition; hybrid dynamical systems; limit cycle stability; linear discrete-time system; necessary and sufficient condition; periodic coefficients; periodic trajectory; qualitative analysis; switched server flow networks; switched server system; Automata; Control systems; Decision making; Discrete event systems; Furnaces; Limit-cycles; Network servers; Stability analysis; Sufficient conditions; Thermostats;

fLanguage

English

Publisher

ieee

Conference_Titel

Information, Decision and Control, 1999. IDC 99. Proceedings. 1999

Conference_Location

Adelaide, SA

Print_ISBN

0-7803-5256-4

Type

conf

DOI

10.1109/IDC.1999.754168

Filename

754168