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**:** 64
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**:** 2016
**:** . . - // . 64. .: , 2016. . 49-64.

** :** 2D-, -, , , , ()

** (.):** 2D-systems, Fornasini-Marchesini model, exponential stability, Lyapunov function, stabilizing control, linear matrix inequality (LMI)

**:** 2D-, --. . . , .

** (.):** The paper considers nonlinear 2D-system described by Fornasini-Marchesini state-space model. Sufficient conditions for the property of exponential stability are developed in terms of vector Lyapunov functions and a converse stability theorem is proved. A form of passivity, termed exponential passivity, is defined and used together with a vector storage function. This technique makes it possible to develop a new control law design algorithm to guarantee exponential stability of the system. As an example the algorithm is applied to a physically relevant case of systems with nonlinear actuator dynamics. Further research will focus on two directions. In earlier work linear Fornasini-Marchesini model was applied to a high-precision rolling system. The results of this paper can be useful to devise a nonlinear control system that will improve the efficiency. Other possible application is related to discrete approximation of Darboux differential equations systems which leads to Fornasini-Marchesini equations. Our results can be applied to problems of this sort.

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