A generating function approach to the stability of discrete-time switched linear systems

Thumbnail Image

Files

HSCC2010.pdf (356.27 KB)

Links to Files

https://dl.acm.org/doi/10.1145/1755952.1755991

Permanent Link

https://doi.org/10.1145/1755952.1755991
 http://hdl.handle.net/11603/35761

Collections

UMBC Faculty Collection
UMBC Mathematics and Statistics Department

Author/Creator

Author/Creator ORCID

https://orcid.org/0000-0003-2172-4182

Date

2010-04-12

Type of Work

conference papers and proceedings
preprints
Text

Department

Program

Citation of Original Publication

Hu, Jianghai, Jinglai Shen, and Wei Zhang. “A Generating Function Approach to the Stability of Discrete-Time Switched Linear Systems.” In Proceedings of the 13th ACM International Conference on Hybrid Systems: Computation and Control, 273–82. HSCC ’10. New York, NY, USA: Association for Computing Machinery, 2010. https://doi.org/10.1145/1755952.1755991.

Rights

Subjects

Abstract

Exponential stability of switched linear systems under both arbitrary and proper switching is studied through two suitably defined families of functions called the strong and the weak generating functions. Various properties of the generating functions are established. It is found that the radii of convergence of the generating functions characterize the exponential growth rate of the trajectories of the switched linear systems. In particular, necessary and sufficient conditions for the exponential stability of the systems are derived based on these radii of convergence. Numerical algorithms for computing estimates of the generating functions are proposed and examples are presented for illustration purpose.