Padé Discretization for Linear Systems With Polyhedral Lyapunov Functions

Author

Rossi, Francesco ; Colaneri, Patrizio ; Shorten, Robert

Author_Institution

Lab. LSIS, Univ. Paul Cezanne, Marseille, France

Volume

56

Issue

11

fYear

2011

Firstpage

2717

Lastpage

2722

Abstract

This technical note has been motivated by the need to assess the preservation of polyhedral Lyapunov functions for stable continuous-time linear systems under numerical discretization of the transition matrix. This problem arises when discretizing linear systems in such a manner as to preserve a certain type of stability of the discrete time approximation. Our main contribution is to show that a continuous-time system and its Padé discretization (of any order and sampling) always share at least one common piecewise linear (polyhedral) Lyapunov function.

Keywords

Lyapunov methods; continuous time systems; discrete systems; linear systems; matrix algebra; piecewise linear techniques; Pade discretization; continuous-time system; discrete time approximation; linear systems; numerical discretization; piecewise linear Lyapunov function; polyhedral Lyapunov functions; stable continuous- time linear systems; transition matrix; Approximation methods; Asymptotic stability; Eigenvalues and eigenfunctions; Linear systems; Lyapunov methods; Numerical stability; Stability criteria; Discretization; Lyapunov function; stability of linear systems;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2011.2161028

Filename

5936107