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Nonlinear ℒ2-gain is a generalization of the well-known finite ℒ2-gain robust stability property for nonlinear systems. Computation of tight performance bounds associated with this nonlinear ℒ2-gain property is key to avoiding conservatism in its application, for example in small-gain based design. In previous work, a number of max-plus eigenvector methods have been proposed to facilitate this computation...
Computation of transient and gain bound estimates via a max-plus power method is considered for a class of nonlinear systems that satisfy a nonlinear L2-gain property. In particular, a max-plus power method is developed for solving an auxiliary optimal control problem that captures worst case behaviour with respect to this nonlinear L2-gain property. This auxiliary problem is formulated so as to ameliorate...
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