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This paper describes a technique for using robust linear estimation on nonlinear systems. This technique provides a means for linearizing the nonlinear system in such a way as to not limit the large signal behavior of the target system. The nonlinearity in the target system must be able to be represented as a piecewise linear function. Furthermore, the H2 and Hinfin robust estimation techniques will...
In this paper, we show discretized Lyapunov functions for various nonlinear dynamical systems by using the method that the authors have proposed. We use Kushner's scheme of difference approximation with directions and Alcaraz et al.'s quantization of Markov processes to approximate Lyapunov equations by linear Schroumldinger-like equations. We construct time-invariant functions concerned with the...
This contribution presents a numerical approach to approximate feedback linearization which transforms a single input nonlinear system into an approximately linear system. Linear matrix equations are explicitly derived for determining the nonlinear change of coordinates and the nonlinear feedback that approximately linearize the nonlinear system. If these linear matrix equations are not solvable a...
This paper proposes to identify a nonlinear system in the nonlinear ARX model from input-output data. A local linear ARX model identification is done by selecting the input and output data around the selected level. By integrating the local linear ARX models, a nonlinear ARX model with parameters nonlinearly depending on the input and output is identified. The dependence of parameters on the input...
We consider the problem of approximately feedback linearizing a multi-input nonlinear system around the equilibrium manifold ?? while making the error terms be of highest order on ??. Necessary and sufficient conditions are given for approximately feedback linearizing the system around ?? with error terms of order ?? on ??.
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