Title :
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
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;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2011.2161028
