Appendix CLYAPUNOV STABILITY
We give here some basic results on stability theory for nonlinear systems. For simplicity we treat only time-invariant systems. For a more general treatment of the subject the reader is referred to [180]. We first need a few definitions from real analysis regarding continuity and differentiability of functions.
C.1 Continuity and Differentiability
Definition C.1 (Continuous function).
Let 
be an open subset of 
. A function 
is continuous at a point 
if, for all ε > 0, there exists a δ > 0 such that, if |x − x0| < δ (and 
), then |f(x) − f(x0)| < ε.
An alternative characterization of continuity is that 
is continuous at x = x0 if f(x) → f(x0) as x → x0.
Definition C.2 (Uniform continuity).
A function 
is uniformly continuous on if for every ε > 0 there ...
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