A scaling and squaring method for the discretisation of positive switched systems

Author

Zappavigna, A. ; Colaneri, P. ; Kirkland, S. ; Shorten, R.

Author_Institution

Dipt. di Elettron. e Inf., Politec. di Milano, Milan, Italy

fYear

2011

fDate

12-15 Dec. 2011

Firstpage

4084

Lastpage

4089

Abstract

In this paper we present a new method for approximating the matrix exponential of a Metzler matrix. This method is useful in discretising switched positive systems. In particular, the method preserves both linear and quadratic stability of the original continuous time system, as well as positivity of states starting for initial conditions in the positive orthant. The usefulness of the method is highlighted by illustrating some of the drawbacks of Padé approximations when applied to positive linear systems.

Keywords

approximation theory; continuous time systems; matrix algebra; stability; time-varying systems; Metzler matrix; Padé approximations; continuous time system; discretisation; linear stability; matrix exponential; positive linear systems; positive orthant; positive switched systems; quadratic stability; scaling method; squaring method; switched positive systems; Approximation methods; Lyapunov methods; Piecewise linear approximation; Stability analysis; Switched systems; Switches; Vectors;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control and European Control Conference (CDC-ECC), 2011 50th IEEE Conference on

Conference_Location

Orlando, FL

ISSN

0743-1546

Print_ISBN

978-1-61284-800-6

Electronic_ISBN

0743-1546

Type

conf

DOI

10.1109/CDC.2011.6160916

Filename

6160916