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The problem of Lurie consists in finding NASC’s for all solutions of the system      { x ′ = A x + b f ( σ  ) , σ  ′ = c T x −  r f ( σ  ) } \{ x’ = Ax + bf(\sigma ),\sigma ’ = {c^T}x - rf(\sigma )\}       to tend to zero as      t →  ∞  t \to \infty       under appropriate conditions on the functions involved. When      f ( σ  ) / σ  &gt; M f(\sigma )/\sigma &gt; M      , for all      σ  \sigma       and a certain      M M      , we obtain NASC’s for the system to be absolutely stable. When      f ( σ  ) / σ  &gt; M f(\sigma )/\sigma &gt; M       as      | σ  | →  ∞  |\sigma | \to \infty      , we obtain conditions for ultimate uniform boundedness of the solutions of the system.

On the condition 𝑐^{𝑇}𝐴⁻¹𝑏+𝑟>0, in the Lurie problem