Nonlinear L2-gain is a generalization of the conventional (linear) notion of L2-gain in which the linear scaling of input energy is replaced by a nonlinear comparison function scaling. In this paper, this nonlinear L2-gain property is formalized as being strictly weaker than the conventional linear property. This is achieved by appealing to existing results in the literature that demonstrate qu...

In the theory of linear H control, the strict bounded real lemma plays a critical role because it provides a connection between the stabilizing solutions to the H Riccati equations and the stability and disturbance attenuation of the closed loop system. Nonlinear versions of the strict bounded real lemma are also important in nonlinear H control theory. In this paper we investigate the extensio...

Nonlinear L2-gain is a generalization of the conventional (linear) notion of L2-gain in which the linear scaling of input energy is replaced by a nonlinear comparison function scaling. In this paper, this nonlinear L2-gain property is formalized as being strictly weaker than the conventional linear property. This is achieved by appealing to existing results in the literature that demonstrate qu...

Nonlinear functions, including nonlinear iterated function systems, have interesting fixed points. We present a non-Lipschitz theoretical approach to nonlinear function system fixed points which generalizes to non-contractive functions, compare several methods for evaluating such fixed points on modern graphics hardware, and present a nonlinear generalization of Barnsley’s Deterministic Iterati...

The bootstrap resampling method may be efficiently used to estimate the generalization error of a family of nonlinear regression models, as artificial neural networks. The main difficulty associated with the bootstrap in real-world applications is the high computation load. In this paper we propose a simple procedure based on empirical evidence, to considerably reduce the computation time neede...

A nonlinear generalization of the family of autoregressive signal models is introduced. This generalization can be viewed as an autoregressive model with state-varying parameters. For such signals, minimum mean-square error prediction can be reformulated as an interpolation problem. A novel interpretation of the signal as a codebook for its own prediction leads to an interpolation strategy rese...