Using multiple Lyapunov function method, the H∞ control theory of switched Hamiltonian systems is discussed. The sufficient conditions in the form of linear matrix inequality (LMI) are presented to guarantee stability of switched Hamilton system. At the same time, an switching law based on switching dwell time is constructed. In order to prove the effectiveness of this conclusion, a numerical simulation example is given, in which the corresponding parameters are calculated by LMI.
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