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Imag 1+G△R 1+GKGw) igure 2.3: Distance to the Nyquist point (1, 0)for the nominal system G(s) and for an arbitrary model in g If K(s stabilizes the nominal system G(s), the condition for K(s) to st abilize all mo dels in g, is that the number of encirclements of (-1, 0) does not change. This is equivalent to the region in the Ny quist plane, covered by all possible Gak(w)not to include(1,0), or that the distance from G(u)to(1, 0)is larger than Gk)e(w) 1+GK(u)>|GK(j)(a), This expression can be rewritten as Gou) 1+GK(w) (u)<1 (28) ju)(a)<1 29 Here T (s)is the closed loop transfer function from reference to output, which is also called the complementary sensitivity function. Hence, if the model uncert ainty is specified by bounding the norm of the mo del deviation, an analytical experession is obtained for robust stability, which offer the possibility to apply the condition directly in design methods that, e. g, involve mI he model uncert ainty is given in other ways, for le by specifying the uncert aunties for amplitude and phase, it is more obvious to apply design methods, where hical il that the uncertainty region for the open loop transfer function does not contain the Nyquist point(1, 0) $ 3;% < ) 2.! 6 6 / ! $2=% ! $2>% $21% 5 6 /