Monotone Piecewise Affine Systems

Author

Aswani, Anil ; Tomlin, Claire

Author_Institution

Dept. of Electr. Eng. & Comput. Sci., Univ. of California, Berkeley, CA, USA

Volume

54

Issue

8

fYear

2009

Firstpage

1913

Lastpage

1918

Abstract

Piecewise affine (PWA) systems are autonomous systems with discontinuous vector fields which are affine ordinary differential equations at the points of continuity. These systems have applications to many fields of engineering, including systems biology and traffic engineering. We define what it means for a PWA system to be monotone, and we provide a set of sufficient conditions for monotonicity of PWA systems with hyperrectangular invariants. Such sufficient conditions are useful for understanding the dynamics of such PWA systems and for designing controllers for qualitative, reference tracking. We apply these results towards the drug-discovery problem for the cancer-related p53 pathway.

Keywords

affine transforms; control system synthesis; differential equations; piecewise linear techniques; vectors; affine ordinary differential equations; autonomous systems; cancer-related p53 pathway; designing controllers; discontinuous vector fields; drug-discovery problem; hyperrectangular invariants; monotone piecewise affine systems; reference tracking; sufficient conditions; systems biology; traffic engineering; Control systems; Differential equations; Drugs; Genetics; Multirobot systems; Stability; Sufficient conditions; Systems biology; Systems engineering and theory; Monotone systems; piecewise affine systems; systems biology;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2009.2023771

Filename

5175392