Extensions of “Padé Discretization for Linear Systems With Polyhedral Lyapunov Functions” for Generalized Jordan Structures

Author

Sajja, S.S.K. ; Rossi, Francesco ; Colaneri, Patrizio ; Shorten, Robert

Author_Institution

Fachgebiet Regelungssyst., Tech. Univ. Berlin, Berlin, Germany

Volume

58

Issue

8

fYear

2013

fDate

Aug. 2013

Firstpage

2071

Lastpage

2076

Abstract

Recently, we showed that certain types of polyhedral Lyapunov functions for linear time-invariant systems, are preserved by diagonal Padé approximations, under the assumption that the continuous-time system matrix Ac has distinct eigenvalues. In this technical note, we show that this result also holds true in the case that Ac has non-trivial Jordan blocks.

Keywords

Lyapunov methods; approximation theory; continuous time systems; eigenvalues and eigenfunctions; linear systems; matrix algebra; Padé discretization; continuous-time system matrix; diagonal Pade approximations; eigenvalues; generalized Jordan structures; linear time-invariant systems; polyhedral Lyapunov functions; Approximation methods; Eigenvalues and eigenfunctions; Linear systems; Lyapunov methods; Piecewise linear approximation; Stability analysis; Switches; Discretization; Padé approximations; nontrivial Jordan blocks; polyhedral Lyapunov functions; preservation of Lyapunov functions;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2013.2246111

Filename

6458987