ABSTRACT
Then we can discribe the system as a equivalent feedback system composed of a linear time-invariant forword block and a nonlinear time -variant feedback block shown in Fig. 4. Based on the theory of Popov hyperstability for the equivalent feedback system shown in Fig. 4 , if the nonlinear time-variant feedback block is satisfied of Popov time discrete integral inequality
and the forword block is strictly positive-real, the system is hyperstable. So the di must be rightly valued to make
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strictly positive-real. The law to regulate the parameters of proportional integral controller satisfied of Popov discrete-time integral inequality is as follows
h!(k) = h[(k-1) + A.r(k)y,.(k-i) hf(k) = p;v(k)y,.(k-i)
i=0,1,2; p;>O; a,~i-~ (16)
Because there is one step nature delay of sampling, the u(k) can not be directly obtained. So the previous value u0 (k) must be employed and the relationship between u(k) and U0 (k) must be found out.
