**:** . .,

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**. :** 04200900023/0064

**:** 27
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**:** 2009
**:** . ., . . / . 27. .: , 2009. .117-168.

** :** , , , ,

** (.):** relay systems, invariance problem, real sliding modes, deep feedback control, linearization by high frequency signal

**:** . . , () , , . . , , . , , .

** (.):** The invariance problem is considered for linear stationary systems with relay control inputs. The classical way of solving this problem consists in using sliding mode control algorithms. When actuators have imperfections (unmodeled dynamics, nonlinearities and so on), the chattering problem arises. In this article the invariance problem is considered for the system with non-ideal relay actuators. There are two approaches to solve the above problem. First method is based on parameterization of nonlinearities of relay by feedback gain coefficients. It is shown that chattering is suppressed completely when feedback coefficients tend to infinity. Another approach consists in using high frequency modulation signal to linearize switching characteristics of relays. Then dynamic compensator approach is utilized for linearized system. The simulation results show the efficiency of the proposed algorithms.

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