On Padé approximations, quadratic stability and discretization of switched linear systems |
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| Authors: | R ShortenM Corless S Sajja S Solmaz |
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| Affiliation: | a The Hamilton Institute, National University of Ireland, Maynooth, Co. Kildare, Irelandb School of Aeronautics and Astronautics, Purdue University, West Lafayette, IN, USAc Mechanical Engineering Department, Gediz University, Izmir, 35665, Turkey |
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| Abstract: | In this note we consider the stability preserving properties of diagonal Padé approximations to the matrix exponential. We show that while diagonal Padé approximations preserve quadratic stability when going from continuous-time to discrete-time, the converse is not true. We discuss the implications of this result for discretizing switched linear systems. We also show that for continuous-time switched systems which are exponentially stable, but not quadratically stable, a Padé approximation may not preserve stability. |
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| Keywords: | Padé approximations Quadratic stability Switched linear systems and discretization |
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