Let $g:\; [0,\; \backslash infty)\backslash rightarrow\; R$ be a positive, continuous, strictly decreasing function with $g(t)\backslash rightarrow\; 0$ as $t\backslash rightarrow\backslash infty$. Let $h:\; [0,\; \backslash infty)\backslash rightarrow\; R$ be a positive, continuous, nondecreasing function. Then there exists a function $G:[0,\backslash infty)\; \backslash rightarrow\; [0,\backslash infty)$ such that
* $G$ and its derivative $G\text{'}$ are class-''K'' functions defined for all ''t'' ≥ 0
* There exist positive constants ''k''₁, ''k''₂, such that for any continuous function ''u'' satisfying 0 ≤ ''u''(''t'') ≤ ''g''(''t'') for all ''t'' ≥ 0,
: $\backslash int\_0^\backslash infty\; G(u(t))\; \backslash ,\; dt\; \backslash leq\; k\_1;\; \backslash quad\; \backslash int\_0^\backslash infty\; G\text{'}(u(t))h(t)\; \backslash ,\; dt\; \backslash leq\; k\_2.$