Robotics Automation

Dynamical Systems with Saturation Nonlinearities: Analysis by Derong Liu

By Derong Liu

This three-part monograph addresses issues within the parts of keep watch over structures, sign processing and neural networks. approaches and effects are decided which represent the 1st profitable synthesis process for associative thoughts by way of man made neural networks with arbitrarily pre-specified complete or partial interconnecting constitution and without or with symmetry constraints for the relationship matrix.

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Additional resources for Dynamical Systems with Saturation Nonlinearities: Analysis and Design

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If an overflow occurs, a number of different actions may be taken. 1 Zeroing overflow substitutes the number zero in case of an overflow (see Fig- corresponding to the overflow level, a is obtained. 2). In two's complement arithmetic, the most significant bits that cause the overflow are discarded. 3. Another way of dealing with overflow is the triangular overflow as the final result does not have overflow. 4). We note that there are other types of overflow arithmetic in use in current technology.

24 For each ~ E A, let C(~) : {g = [Xl,''" , Xn]T ~ ~n: I < < 1 if ~i = o, and xl = (i if ~'i ¢ 0}. Suppose t h a t ~ E A,~ and a E P(n) such t h a t G(1)=0, 1

We now show that under the conditions of our theorem, once x(t) leaves OD ~, it will never enter OD ~ again. Since x(t) will not always stay on OD ~, without loss of generality, we assume that x(0) E (D~) °. (t)=~*x(o). ~ollx(o)lloo. Using the fact that (see [28], page 59) for any t _> 0 and any p _> 1, we have since #~(A) < O. , when x(0) E ( D ' ) °, x(t) will never reach the boundary of D ' . 10) for all t >_ 0 when x(0) E (Dn) °. Hence, x(t) ---* 0 as t ---* oc, since ReA(A) < O. Summarizing, above we have shown that (i) x(O) ~ D n is not allowed; I 27 (ii) if x(tl) C OD ~, x(t) cannot stay in OD ~ for all t > t~; and (iii) once x(t) is in (D~) °, it will never enter OD ~ and x(t) ---* 0 as t ~ oe.

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