Error bounds of piecewise-linear approximation

A description is given of upper bounds on the error caused by piecewise-linear approximation of a nonlinear element T in a feedback loop, where T represents a nonlinear operator whose domain is the set of the z-transform of the sampled sequences. Let W' (z) be the solution of W' (z)=X (z)+H (z) T' (W' (z)) which approximates the exact input-output relation W (z)=X (z)+H (z) T (W (z)). In order to discuss an upper bound on the norm of the approximation error // W' (z)-W (z) //, the generalized parametric norm of an operator is proposed. The obtained upper bound is sufficiently small compared with a bound by the conventional norm in many cases.<
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