# Nonlinear $L_2$-gain suboptimal control

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## Abstract

A method of solving the nonlinear local $L_2$-gain suboptimal control problem based on the chain-scattering approach is proposed. This problem requires $L_2$-gain of the closed loop to be less than one and closed loop internal stability defined in the small signal input-output sense. We obtained sufficient conditions for the existence of a suboptimal controller in terms of state-space description of the plant as well as a local state-space parameterization of a class of controllers solving the local $L_2$-gain suboptimal problem. The design procedure is demonstrated in a numerical example.

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