Title :
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
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;
Conference_Titel :
Decision and Control and European Control Conference (CDC-ECC), 2011 50th IEEE Conference on
Conference_Location :
Orlando, FL
Print_ISBN :
978-1-61284-800-6
Electronic_ISBN :
0743-1546
DOI :
10.1109/CDC.2011.6160916
