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The problem of H ∞ control of switched nonlinear systems in p -normal form is investigated in this technical note where the solvability of the H ∞ control problem for individual subsystems is unnecessary. Using the generalized multiple Lyapunov functions method and the adding a power integrator technique, we design a switching law and construct continuous state feedback controllers of subsystems explicitly by a recursive design algorithm to produce global asymptotical stability and a prescribed H ∞ performance level. Multiple Lyapunov functions are exploited to reduce the conservativeness caused by adoption of a common Lyapunov function for all subsystems, which is usually required when applying the backstepping-like recursive design scheme. An example is provided to demonstrate the effectiveness of the proposed design method.
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Long et al. (2012) studied this question.
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