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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 has distinct eigenvalues. In this technical note, we show that this result also holds true in the case that has non-trivial Jordan blocks.
In this paper we show that certain piecewise-linear Lyapunov functions are preserved for LTI systems under Padé approximations. In particular, we present a simple method to find a piecewise-linear Lyapunov function that is so preserved under the Padé discretization of any order and sampling time. This result may be of interest in the discretisation of switched linear systems for both simulation and...
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