Abstract
We treat the problem of constructing Lyapunov functions for systems which are, by assumption, exponentially stable. The construction we present results in a larger set of functions than those obtainable by previously known methods. A useful property of the proposed Lyapunov functions is that they preserve information on the rate of exponential convergence of the system. Some useful applications are given.
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The first author was supported by the US National Science Foundation under Grants MSM-87-06927 and MSS-90-57079. The activities of the second author were performed during a stay at the School of Aeronautics and Astronautics, Purdue University, and were supported by Consiglio Nazionale delle Ricerche, under Grant 203.07.17.
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Corless, M., Glielmo, L. New converse Lyapunov theorems and related results on exponential stability. Math. Control Signal Systems 11, 79–100 (1998). https://doi.org/10.1007/BF02741886
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DOI: https://doi.org/10.1007/BF02741886