Padé discretization for linear systems with polyhedral Lyapunov functions
Rossi, F. and Colaneri, P. and Shorten, R. (2011) Padé discretization for linear systems with polyhedral Lyapunov functions. IEEE Transactions on Automatic Control, 56 (11). pp. 2717-2722. ISSN 0018-9286
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.
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