**:** ..,

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**:** ( ). I

**:** 28
**:**
**:** 2010
**:** .., .. ( ). I / . 28. .: , 2010. .89-125.

** :** , , , , ,

** (.):** closed-loop system, causality, stability, distributed dynamic systems, a linear heat conduction object, complex variable theory

**:** , . .

** (.):** We obtain the estimates of the norms of the boundary influences-to-temperature operators for two special cases of boundary conditions for the stable one-dimensional finite-length object of heat conductivity. These estimates are used to find the sufficient condition of causality and stability for the non-linear feedback control system.

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