On the control of instable systems (Q1074852)

The results are devoted to the investigation of the limiting behavior for \(\epsilon\) \(\to 0\) of the sequences \(I_{\epsilon}\), \(u_{\epsilon}\), \(y_{\epsilon}\) where \[ I(u_{\epsilon},y_{\epsilon})\leq I_{\epsilon}+| \epsilon |,\quad u_{\epsilon}=\epsilon Ay_{\epsilon}+| y_{\epsilon}|^ n, \] \[ I(V,Z)=\| Z-Z_ d\| +N\| v\|,\quad 0\leq N<\infty, \] \[ I_{\epsilon}=\inf \{I(v,z)| \quad v=\epsilon Az+| z|^ n\},\quad 1\leq n<\infty, \] A being an arbitrary linear operator \(A: L^{rn}\to L^ r\), D(A) dense in \(L^{rn}\), \(Z_ d\in L^{rn}\), \(Z\in D(A)\), \(v\in U\subset L^ r\).