Approximation of nonlinear ℒ2-gain bounds via a max-plus method

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 a specific continuity problem that arises in the computation of these estimates. A simple example is presented to illustrate how these estimates may be recovered from the solution of this auxiliary problem.