Analysis of Discrete-time Nonlinear l2-gain Bounds via Dynamic Programming

Abstract

In the input-output framework, the notion of nonlinear ℓ2-gain extends the classical (linear) finite ℓ2-gain in order to apply ℓ2-gain analysis techniques to a larger class of nonlinear systems. Obtaining tight estimates of the comparison function bounds for the nonlinear ℓ2-gain property is particularly important in small gain design. In this paper, we present two optimisation-based formulations that characterise these bounds for discrete-time nonlinear systems satisfying the nonlinear ℓ2-gain property via dynamic programming.